OK, so the "dead trigger" and the firing pin drag/broken FP are two (2) separate issues?A dead trigger can be caused by different issues but in general it means that the actual trigger is in one form or another disconnected from the action, hence rendered useless.
In this case it does not relate to the breaking of the firing pin.
Most likely it is caused by the break-down design flaw in the P365.
Check out this video where the SIG rep has to push the safety back down with her nail at 1:29 in order to get the slide all the way back on. If you don't know about this issue and slam it, it surly can cause that dead trigger problem.