In my experience, for ‘standard’ RNP approaches (I.e. not A-RNP or AR), the FMC displayed RNP changes to 0.3 at the FAF. The aircraft could be in on-approach logic prior to this waypoint but the RNP does not change.
It changes to whatever the RNP procedure was designed to. I have seen 0.1, 0.3, 0.5.