I think creating a custom fsm state for this would be much of a hassle (and you will need to redesign the FSM … ).
Here are some solutions (apart from changing the code or having an option in FSMOwner):
If the “GoToScreen” action task that is used in all “leaf” states is custom (probably is), then you can change it so that it never finishes (by not calling EndAction).
You can add the “Run Forever” action task in all states that you want to keep running forever and thus the FSM does not finish for those states.
If the reason you want to keep the FSM alive/running is because of the Parallel state (which was replaced by the OnFSMUpdate by the way), I can add an option in the node’s inspector so that it is always running and thus once again the FSM is never considered finished when such OnFSMUpdate node is present.
If the above is not the reason, and you simply want to keep the FSM alive no matter what, following is a custom FSM node code that will keep running forever and will have the same effect as having an option in the FSM as suggested above: