will cortex m3/m4 enter a lockup mode if a serious fault happened while FAULTMASK is set

Greetings,,

what happens if FAULTMASK is set in cortex-m3/m4 and one or more serious fault happened like bus fault, MPU violation, invalid instruction, stack corruption.. etc will the processor enter a lockup? if not what would be the status of the processor? what will happen to the currently executed program/code.. since HardFault handler is not executed to remedy the issue.. if you can elaborate and give as much explanation and details as possible and if you can share some cases and examples it would be very appreciated..

Thank you..