To clarify: By something that isn't supposed to be killed I mean things that are out of mortal's power range.

As far as I can tell this isn't a system specific problem. I experienced the same thing with Call Of Cthulhu as well as World Of Darkness as well as D&D with a variety of people. I always seem to get a player who plots to kill Cthulhu or Cain or Lady Of Pain.

I don't want to pull the 'Stop talking about it or I'm kicking you out' since it is rarely done during the session time. It usually comes up after a gaming session.

I tell them no and the rest of the group tells them it is impossible as well. This does not stop the player from arguing about how it should be possible despite everyone telling them how their plans won't work. I feel that after each such conversation my players feel less attached to the game.

What I wish to ask is how can I deal with this argument that seems to crop its head up no matter the system nor the group without threatening people?

To answer the comments.

It is impacting my game in the sense that after the game the person in question starts talking about how he has a new plan to kill X and the groups focus shifts from talking about the next session and discussing the cool moments in the game to explaining how his plan will not work which makes everyone miserable.

Also the player in the other question does this too but it is not specific to him. I just recognized the pattern happening over and over again with different situation.

A revamp of Session Zero should resolve this

I don't want to pull the 'Stop talking about it or I'm kicking you out' since it is rarely done during the session time. It usually comes up after a gaming session.

You've got a bit of an expectations mismatch. What you need to do is to revisit Session Zero with everyone before the next play session starts. You believe that you have the support of all of the other players. You are the GM:

1. GM: OK, let's get on the same page. I am not running a game where
   Cthulu/Lady of Pain/Cain (or whomever) can be killed. Attempts to
   kill them will always fail. No dice rolled, no skill combinations,
   no cool moves. This entity is as permanent as Gravity is here on
   earth. Do we have any questions on that?


2. Players, 1 through X: Offer opinions.


3. GM: OK, let's vote on this.


4. Vote.


5. If as you say, the other players are on your side, you then tally up
   the votes.


6. 
   

   GM: OK, the vote is 5 to 1 that this is the game we are playing.
   Now let's play. I will not entertain any further discussion of this
   topics, since it has been decided here and now.

   
   
   

   If they ever bring it up again, you must remain firm.

   
   
   

   "Sorry, we voted on this, no. That's a closed issue. What else do you want to talk about?"

   
   

And stick to your guns.

Your problem isn't whether or not this thing can be killed. The problem is that this player does not accept your ruling as a GM, and is also not accepting the consensus of the other players at the table.

Your other problem? Your group's inability to establish a small group consensus.

For further tools used in building small group consensus, read here.

Caution

If the vote goes against you, the GM, then you need another session zero to figure out what game you all are playing. Work out an agreement with the other players. If you have the entire table wanting to kill the unkillable, and that isn't the game you want to run, don't run it. Ask someone else to GM.

Experience

Lots of experience in sticking to my guns after making a decision as GM. And a few experiences where a GM stepped down when the group consensus went in a different direction. (Common observation by GMs in cases like this is something like "I don't get paid enough for this aggrivation.")

The conversation typically goes something like this:

"Neat idea, it doesn't work that way in this game world. No, this isn't negotiable. Another GM may like that, but not this one."

I've also seen loads of DMs and GMs do the same thing. Eventually, say No and back it up while getting the support of the other players. It's a thing that each GM now and again needs to do.

I have a personal favorite line I give to players who are trying to argue about this:

If you encounter [insert unimaginably powerful being here] in-game, you're welcome to try your plans.

And if they persist...

Y'know, honestly? I'm not interested in arguing about this. Feel free to plot and plan all you like, if you encounter [PC's future cause-of-death] in-game, you're welcome to try your plans. At that time if I, as the DM, figure your idea would work...then cool! But I'm not going to tell you, cuz that would be spoilers. Just...bear in mind...if your plan wouldn't actually work against that creature as established in the lore, your character is not likely to survive the attempt.

As you have stated, this player is not actually disrupting the game itself with their planning and plotting--so it seems to me that the main thing you want is to terminate the arguments. The simplest way to do that is to not argue.

As soon as you engage this person on their myriad ideas to shoot them down, you're prolonging the discussion. This is a similar effect to the "Don't feed the trolls" policy across the internet in general. By engaging with them, it feeds the argument and makes it go on longer. You don't have to use my line...but when you do not want to engage in a debate, dismissing it is frequently better than engaging with it.

Once done...you have two basic options.

Option A: Simply make sure the party doesn't encounter one of these beings. At that point, it's all theorycraft at that point and thus harmless. And by refusing to engage in the debate (and getting the rest of your players to do the same), it's essentially diffused.

Option B: Should the player encounter that being and try their plans...let things play out as they ought to. Player's character gets eviscerated, eaten, locked in perpetual orbit around a point three seconds to the left of the future, mazed, or otherwise thrashed. Expect protesting and whining, and having to put your foot down as the arbiter of the rules.

A line I dropped in that case was

[Horrible murder machine] has lived for eons--do you really think you're the first person to try that?

Player wasn't particularly happy with me, but I moved things along, they rolled up a new character, and we carried on.

Since it's not happening in session time, this isn't really a gaming problem. You have folks who enjoy arguing for the sake of arguing, and happen to choose impossible tasks in a game as their preferred argument.

If you don't like hanging out with argumentative people, don't try to win unwinnable arguments, stop inviting them to your house. The problem with arguments of the form you describe is that, being an imaginary world, they can always imagine some way of doing what they want to do, they just have to ignore the fact that they're not the sole arbiters of how the world works. You can't win this argument. Don't have it.

If you don't want to kick them out immediately, the list of approaches to try would be something like:

1. Explain that in your game world, these creatures are simple facts of the world, on the level of elemental forces. Sure, you can fight them, but it's like fighting the Sun, the wind, gravity, electricity, etc.; there's no practical solution available to mere mortals. If they want to run their own game, they can do it their way, but it's a conversational dead end in your game. Then change the subject.


2. Point out that argumentative navel gazing isn't fun for anyone else. For the people it is fun for, ask they deal with it on their own time.


3. (In private) Make point #2 more directly, and note that you can't keep inviting them if they're going to ruin things for everyone else. Yes, it's a threat. But a threat is better than ejecting them without warning.


4. Stop inviting them to the game. Feel free to explain why if you like.

Note that you can do #3 in the form of #4 if you prefer to avoid threats. Tell them you're not inviting them back, explain why, and leave the ball in their court. If they promise to stop and request an invite back, go ahead and offer it to them if you like. It's the same result as a threat, but one in which they have to take the initiative to change their ways.

I'm sorry there isn't a better way to handle this. People are harder than games, and sometimes the answer is "stop hanging out with people that prevent you from enjoying yourself."

I've run and more often been in games where certain entities are just unkillable either because it just can't be done by anything the players have access to, can't be done at all, or the lesser case where the infinitesimally unlikely success would mean the end of the game. (Depending on your implementation, think "Killing Dworkin," in an Amber game.)

Contrary several of the other answers, I don't regard this as necessarily a Session Zero concern. (It can be if you want it to, I just don't think it is necessarily so.) I think it's actually a bad idea to put this up a vote.

What I've seen done, and done myself, is a two-tier approach:

• Tier One: Impress the information on the players through the NPCs. If enough NPCs in a position of knowledge and power declare something to be impossible, and describe the reasons why ("Dworkin is one with the Pattern, killing him destroys everything. Even Brand didn't do that, he just damaged it/them,") it usually sinks in. Usually.



• 
  

  Tier Two: Impress the information on the players directly, as with other extreme, fundamental misapprehensions about the game. "Look, This is not fair or right. I cannot let you continue to operate under the impression that this thing is possible. It's not. It's not a matter of finding a way to do enough damage or to bypass their protections, or some other matter of mechanics. This isn't about mechanics, because there is no mechanic to do this. You're not playing in a game where this is possible, and it's not open to negotiation. The best case outcome is your character's death."

  
  
  

  (At heart, Tier Two is not unlike the speech I give to Pollyannas (polly-hobos?) who find their way into a dark and gritty campaign, or to murder-hobos who are playing in a game where the forces of civilization will hunt them down and kill them for egregious behavior: "You are not playing the game you think you are, and you are picking a fight you can not win. And possibly dragging the other characters into it against their will." Being really blunt and up front about that is vital.)

  
  

In my grumpy dotage, I tend to cut to Tier Two pretty quickly. I really don't want my players laboring under bad beliefs about the game, and mostly players are receptive if you don't overdo the bluntness and pole vault into rudeness or abuse. But I'm sorry to say I've seen that fail, too. It does not end well. It's usually suicide-by-GM, or the player leaving the game by mutual consent because they're not going to get from it what they really want to get.

Don't fear the planning.

Personally, I believe that as a GM you should never fear the PCs planning something, or setting themselves an end-goal in the campaign. In fact, you should rejoice at the fact. Long-term plans give your players focus and makes them 'buy in' the campaign.

Make it too troublesome

However, I do think I understand your dilemma. There are some monsters/creatures which should always be too strong to kill, and if your players ever attempted it, they would fail horribly. Sometimes, you'd rather avoid a TPK and not have the BBEG fight the party. In that case, you should NEVER take the option of fighting the BBEG away from the players, but rather take away one of the things that the players need to battle him, even though they want to. I'll give you some examples, and you should figure out how to best do it for your campaign.

Luckily, these are also the hurdles that need to be overcome for any great BBEG.

• 
  Reach: First of, the BBEG is always a 'final boss' or big enemy general, so it would never be at easy reach of the players. He would always be in either a different continent, behind a whole army of minions, or at the very end of the dungeon. A different plane of existance or a hidden place unreachable by mortals, in eternal slumber would also work wonders.


• 
  Motive: This might be counter-intuitive, but ussually players have a reason for wanting to defeat stuff (unless they are all murderhobbos, but that's a different problem altogheter). Maybe the BBEG is... bad, or hoarding a great reward... take that away, and the players will just go 'meh', whatever.


• 
  Gravity: This refers to the players being powerful/annoying/important enough for the BBEG to even bother fighting them. Would a god interrupt his busy day to go smite every single mortal that curses it? No, of course not. Would a powerful lich go out of his way to fight a bunch of wannabee adventurers? Not likely. Would a general rush across the field of battle, abandoning his troops and orders to kill off one or two grunts? Hardly. Having the BBEG simply ignore the taunts and challenges of the party, or having him toy to the extreme with them, even to the point of killing and reviving them as a joke is plausible.


• 
  Hope: C'mon, we all know that if they don't think they have a chance to win that they will fight it. So the first thing is to take away that hope of winning. If they decide to embark on a quest to revive Kh'thulu in order to kill him, allow them. But during their journey have stories prepared to telll them of the horrors they will face. Get NPCs to push the atmosphere of the campaign towards the hopeless doom that it should be. Have, as the players progress, the sky turn crimson, the earth shatter and demons come loose, and have heroes that dwarf them in power and status come out and meet them in a desperate attempt to stop their madness.

Set the right atmosphere

However, if your PCs aren't taking your BBEG seriously, it might have something to do with the mood and character you're portraying for it. When talking about important NPCs, I generally try to set the mood of the whole encounter, starting by describing the room and the stance/actions the NPC is currently doing. If you want to make the players get the hint that the NPc should be taken seriously, have them roll a WIS saving throw upon seeing it, and on a fail, drop down to their knees and cower in horror.