When you start a local shell, you can generate some session identifier (export DURABLE_SESSION=$RANDOM) and put it in your environment. Then have your ssh client send it to the server with "-o SendEnv DURABLE_SESSION". One question is when does sshd know when to ditch interrupted sessions.
You can always manually interrupt an SSH (or Telnet) session using the following key sequence: This sequence is caught by the SSH client to force a session disconnect.
My question raised the point that the server would not be able to tell the difference, after an interruption, between session state that the client will hope to resume and session state that should be discarded. That state would accumulate until some routine cleared it out.