Can an airliner complete a flight with one pack inoperative?
The 747-8 has three packs, and it is feasible to complete the flight with one of them inoperative (in case of aircraft with two packs, cabin altitude can be maintained win any one). The following is taken from the Minimum Equipment list of 747-8:



Screengrab from 747-8 MEL

As can be seen, flight is possible with some limitations. In case of a failure in-flight, the flight crew would follow the applicable checklist and decision will be taken whether to continue the flight or not (as altitude is limited). In case of failure, the appropriate warning message will be displayed (the pack, sensor, valve etc.)