If it happens that the process setting the alarm for `exit_timeout` crashes and another one is in lock/busy loop, then it is somehow really bad luck. Not sure what would be an easy solution, maybe having a watcher process not doing anything, not even at startup/shutdown (PRs are welcome). If it is something that happens always, then there is another crash causing this behaviour.
Maybe systemd has some option for `stop` to `kill` it after a while if the process refuses to stop.