Is baggage always offloaded when a passenger does not travel?
Normally, baggage takes much longer to switch flights than self-loading cargo, so your scenario is highly unlikely.

In the event of a passenger missing and his/her baggage already on board, all bags need to be unloaded until the orphaned bag is found. When ULDs are used, those must be unloaded first and are then unpacked, mostly on the apron next to the aircraft.

Waiting for the missing passenger is an open-ended game. At some point, you must decide on a course of action with a fixed exit so you can move on. 

Normally, every airline is required to unload an orphaned bag. I am sure some are more strict about this than others.