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After having read the disturbing

https://en.wikipedia.org/wiki/1999_South_Dakota_Learjet_crash

I'm left with the question as to why the computer allows for the autopilot to be disengaged when there is no pilot input.

Why doesn't it engage the stick shaker and alarm as normal, but maintain control until pilot input is received, or require the pilot to manually disengage the autopilot?

I'm not a pilot, so I'm sure there is a good reasoning behind this. However, from my own naive perspective this is why it seems foolish to automatically disengage the autopilot:

This is what happened after the autopilot was disengaged:

"The target is descending and he is doing multiple aileron rolls, looks like he's out of control...in a severe descent, request an emergency descent to follow target."

Imagine that the crew did regain consciousness, they would find themselves in a disorienting situation, with an aircraft possibly damaged from aerodynamic stress when approaching mach 1 in an uncontrolled nose dive. This, compared to the autopilot simply maintaining attitude as best it can.

Until finally, this: "the aircraft hitting the ground at a nearly supersonic speed and an extreme angle."

The alternative being, with no pilot input that the aircraft would have maintained a somewhat stable attitude, deploys its landing gear, flaps, and prayed for the best -- that there just happens to be a fairly smooth piece of land, with no major obstacles in the way?

Now, I'm aware that all six on board were dead before the plane crashed. That doesn't mean there are no situations where a controlled crash landing is not preferable to an uncontrolled crash.

I'm not an avionics software engineer, so forgive me if I don't appreciate the complexity of the task -- but as a software engineer and someone with an IT education it seems to me almost trivial to extend the functionality for the aircraft to accommodate for this scenario with a mostly hard-coded procedure---yes, blindly landing at whatever is there and hoping (and with the system being extended with visual processing, perhaps, in the future). While I'm not even going to sketch a full proposal for such an extension here, it is part of my motivation for asking this question in the first place, so I'm simply mentioning it as that.

I can also mention, although I'm sure anyone qualified to answer this question will know about this case (and know it far better than I do), the Cornfield Bomber https://en.wikipedia.org/wiki/Cornfield_Bomber so if this is possible without any help from the computer, surely it would be possible with help, even from a computer that only has basic instruments (altitude, attitude, etc.) and no vision, yet simply attempts it "blindly" as far as visual processing is concerned.

Please keep in mind that I'm under no illusion that the plane will land without a scratch. This is a game of statistics, such as all safety procedures, and it seems (naively, I'm sure) that this might increase the chances of survival by some (probably slim) margin.

My own attempt at an answer:

I can only imagine that the reason such functionality doesn't exist, is because it is so rarely useful and considered too much of a curiosity. However, other crashes that also appear to be highly unlikely in general, have seen changes enforced in the aviation industry. So this isn't really a good answer.

The only other thing I can think of, is the omnipresent fear of AI. The idea to implement some AI, that could potentially, when given full authority of the plane, glide it into a building unintentionally, is just unthinkable for obvious reasons. While I sympathize with this view, I don't see why this is more likely than it happening with a plane flying without such a simple AI---both the AI and the completely uncontrolled plane would be flying just as blindly, both at risk of hurting innocent bystanders. The only difference is that the AI assisted plane flying autonomously (despite mostly blindfolded) does have a marginally higher chance of allowing for some survivors.

The "autopilot" is a fairly basic control system. Usually it is composed of just a few components (logically speaking) like a wing-leveler, heading mode, and altitude mode. The autopilot can control the aircraft usually through servo's connected to the control cables or through the hydraulics. External systems can feed into this to do things like follow a descent path, follow GPS/VOR routes, etc. The autopilot itself is basic.

The autopilot is designed to fly an aircraft that does not otherwise have any other issues. The autopilot is not designed to fly outside of normal operating circumstances. This means that when some kind of abnormality is detected (usually through the autopilot hitting its programmed limits) it will automatically disconnect.

In the Learjet case you cited, the autopilot continued to maintain altitude after the engines failed, but because maintaining altitude without engines means your speed will decrease, the autopilot disconnected before the aircraft stalled rather than fighting the pilot through a stall. It assumes that it is safer to automatically hand-off than require the pilot who is now trying to stabilize the aircraft to also have to worry about disconnecting the autopilot.

Most autopilots give some kind of warning that they've disconnected. This can be things like a chime, voice alert, stick shaker, etc. It's the autopilots way of saying "I've reached the limits of what I can control, you need to take over now". Otherwise it could potentially make a situation much worse.

The cornfield bomber was not on autopilot when it crashed. It just regained stability as a result of the ejection and remained on a fairly level (but descending) path until it bellied into a field (and continued to run/move for quite some time).

The autopilot is designed to do exactly what it's told, until it can no longer safely do so. At that point the situation is beyond what the autopilot is designed for, so it hands control back to the pilots. Even modern autopilots aren't designed to do much descision-making on their own, let alone a Learjet designed in the 1970's.

Adding some sort of functionality to "fly the plane down" in such a situation would add complexity to the system for very little benefit. This sort of situation is fairly rare. And most of the world is water, with much of the rest being not very flat. It's extremely unlikely that for all that effort such a system would be able to make any survivable landings.

And even if it could make a survivable landing, we're talking about crew and passengers that could have been passed out for hours, and might not surive that anyway. Perhaps there's some value in a sort of "dead-man's switch" that would automatically bring the plane down if the pilots fail to respond, but this has most of the same issues above.

There's also the issue of adding yet more automated features to the flight controls. How do we handle situations where this malfunctions, and starts unexpectedly descending the plane for no apparent reason? That sort of thing would be especially unpopular right now.

Some fighter jets do have a system called Auto-GCAS that is designed to stop an unconscious pilot from flying into the ground, but that's a much more simple problem to solve than getting on the ground safely.

The general philosophy is that autopilot is a tool, not an extra pilot, and as such, it disengages when anything goes seriously wrong. Inertial sensor failure? Engine loss? Unusual attitude? Hand control back to the pilots with a nice warning sound. This option isn't taken lightly, especially in high-workload situations like landing, but it's the general solution to rare conditions.

Yes, it may seem from a software perspective like a small feature to add robustness here and there's certainly room for innovation, but the cost and liability to develop for rare and even dangerous situations is generally not worth the rare benefit it provides. For example, here the autopilot disengaged because the plane went below stall speed or vmin. The standard solution to a stall is to descend and increase throttles to build up speed again, but automated stall recovery has complications like traffic and terrain avoidance, and thrust-management integration. Automated stall recovery is especially tricky when you have no fuel as in this incident, or back in 1999 when enhanced TAWS and TCAS II was fairly new and before GCAS.

Additionally, preventative solutions now exist that make the cost-benefit analysis here even more lopsided. First, it should be noted that in general, planes are stable and flying without pilot or autopilot input causes the plane to fly more or less straight and level, although that did little good here. Automated pitch-based low-speed protection or AoA protection are standard on some aircraft like Dassault jets. Airbus and other companies have developed a rapid/emergency descent feature to handle incapacitated pilots due to depressurization. Fighter jets are developing an auto-GCAS as fooot has mentioned that's already saved the lives of some incapacitated pilots.