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Two programs use a TCP connection (3-way handshake) to open, communicate, terminate the connection and open a new connection. If a FIN message sent to shut down the first connection is duplicated and delayed until the second connection has been established, then delivered, will the new connection be terminated?

No for at least two reasons:

• source and destination ports


• sequence number

Even though the pair source/destination ports is same as the first connection, the sequence number is unlikely to be same because the initial sequence number of a connection is supposed to be random.

The RST flag isn't seq nb dependent. Assuming the pair src/dst ports is same, a previous RST flag would terminate the session.

Thus, there is a very low probability that a duplicated FIN packet of another old already terminated session would terminate the new one.

A FIN for one connection has nothing to do with a second connection. Remember that a connection is identified by two sockets (source and destination). Either you would have two separate connections where one of the sockets in the pair identifying the connection is different, in which case, the two sockets are completely separate, or you would be trying to establish an existing connection, which should result in a RST.

Basically, your situation could not occur because the two connections are entirely separate, or the second connection could not be established until the first connection is completely closed.

RFC 793, Transmission Control Protocol is the definition of TCP, and it explains how it works:

Multiplexing:

To allow for many processes within a single Host to use TCP
communication facilities simultaneously, the TCP provides a set of
addresses or ports within each host. Concatenated with the network and
host addresses from the internet communication layer, this forms a
socket. A pair of sockets uniquely identifies each connection. That
is, a socket may be simultaneously used in multiple connections.

The binding of ports to processes is handled independently by each
Host. However, it proves useful to attach frequently used processes
(e.g., a "logger" or timesharing service) to fixed sockets which are
made known to the public. These services can then be accessed through
the known addresses. Establishing and learning the port addresses of
other processes may involve more dynamic mechanisms.

Connections:

The reliability and flow control mechanisms described above require
that TCPs initialize and maintain certain status information for each
data stream. The combination of this information, including sockets,
sequence numbers, and window sizes, is called a connection. Each
connection is uniquely specified by a pair of sockets identifying its
two sides.

When two processes wish to communicate, their TCP's must first
establish a connection (initialize the status information on each
side). When their communication is complete, the connection is
terminated or closed to free the resources for other uses.

Since connections must be established between unreliable hosts and
over the unreliable internet communication system, a handshake
mechanism with clock-based sequence numbers is used to avoid erroneous
initialization of connections.

-and-

Reset Generation

As a general rule, reset (RST) must be sent whenever a segment arrives
which apparently is not intended for the current connection. A reset
must not be sent if it is not clear that this is the case.

There are three groups of states:

1. 
   

   If the connection does not exist (CLOSED) then a reset is sent in
   response to any incoming segment except another reset. In
   particular, SYNs addressed to a non-existent connection are rejected
   by this means.

   
   
   

   If the incoming segment has an ACK field, the reset takes its
   sequence number from the ACK field of the segment, otherwise the
   reset has sequence number zero and the ACK field is set to the sum
   of the sequence number and segment length of the incoming segment.
   The connection remains in the CLOSED state.

   
   


2. 
   

   If the connection is in any non-synchronized state (LISTEN,
   SYN-SENT, SYN-RECEIVED), and the incoming segment acknowledges
   something not yet sent (the segment carries an unacceptable ACK), or
   if an incoming segment has a security level or compartment which
   does not exactly match the level and compartment requested for the
   connection, a reset is sent.

   
   
   

   If our SYN has not been acknowledged and the precedence level of the
   incoming segment is higher than the precedence level requested then
   either raise the local precedence level (if allowed by the user and
   the system) or send a reset; or if the precedence level of the
   incoming segment is lower than the precedence level requested then
   continue as if the precedence matched exactly (if the remote TCP
   cannot raise the precedence level to match ours this will be
   detected in the next segment it sends, and the connection will be
   terminated then). If our SYN has been acknowledged (perhaps in this
   incoming segment) the precedence level of the incoming segment must
   match the local precedence level exactly, if it does not a reset
   must be sent.

   
   
   

   If the incoming segment has an ACK field, the reset takes its
   sequence number from the ACK field of the segment, otherwise the
   reset has sequence number zero and the ACK field is set to the sum
   of the sequence number and segment length of the incoming segment.
   The connection remains in the same state.

   
   


3. 
   

   If the connection is in a synchronized state (ESTABLISHED,
   FIN-WAIT-1, FIN-WAIT-2, CLOSE-WAIT, CLOSING, LAST-ACK, TIME-WAIT),
   any unacceptable segment (out of window sequence number or
   unacceptible acknowledgment number) must elicit only an empty
   acknowledgment segment containing the current send-sequence number
   and an acknowledgment indicating the next sequence number expected
   to be received, and the connection remains in the same state.

   
   
   

   If an incoming segment has a security level, or compartment, or
   precedence which does not exactly match the level, and compartment,
   and precedence requested for the connection,a reset is sent and
   connection goes to the CLOSED state. The reset takes its sequence
   number from the ACK field of the incoming segment.