Are these reroutes happening in flight, via ACARS, or via phone call? As far as I know there is no obligation to answer your phone while on a layover, is there?

Before ACARS existed, the company was known to have the gate agent meet the inbound crew with a reroute message in hand, to deliver to them on arrival, especially when they were short of Flight Engineers, they would try to hand him an assignment for the next day. Some engineers would drop the aft air stairs (727) and leave the aircraft via the back, rather than get tagged by the agent for another trip.