I wouldn't know the cabin pressure controllers of all aircraft, but I fly the B74 and when the auto pressurization controller goes on vacation, then the cabin is controlled MANUALLY; the 2 cabin outflow valves have back-up DC motors which are operated MANUALLY.
If ever or whenever as a passenger you fly into El Alto at 13,310' [AA operates B757] you won't see cabin oxygen masks drop from the ceiling, and you won't see people walking around with portable oxygen masks.