I am facing one issue with process initiator deactivation.

The process won't stop working exactly, but certain things that happen in the "initiator" context will start failing (and it can cause a weird error message).  This is a core reason why I tend to design subprocess trees to initiate as "publisher", so only top-level process contexts are running as "initiator" (and even this approach is imperfect, but usually "good enough").  If there's a certain initiator who has loads of instances running in their name, then usually the best solution is to not deactivate them, but take certain other approaches when they no longer need access to their account.