Three phase commit : study case
I found the answer consulting the book "Distributed System : Principles and Paradigms" (Andrew S. Tanenbaum - Maarten Van Steen). First of all it is possible to continue just because 3PC is non-blocking protocol by definition. A processor can reach the state “PRE-COMMIT” only if the coordinator was in state “PRE-COMMIT” (thus each processor sent a COMMIT request), so the crashed processor could not be for sure in state “INIT” nor in "ABORT", but at least in the state “READY”. Anyway, all the “alive” processors, after seeing the “PRE-COMMIT”, will go in “COMMIT” state.