Has a train ever arrived AFTER the next day's train?
I can't site any specific such occurrence's, but I can see a train getting stuck at a major obstruction, with the only alternate route to go hundreds of miles back to a detour point. The following day's train, could be detoured and be at that point much sooner. Usually, if the train running the opposite way hasn't already cleared that obstruction, they will turn the two trains, and use chartered buses as a 'bridge' around the obstruction. If the train going the opposite way is already by that obstruction, that plan would not work.I speculate that Amtrak would just combine trains at that point...but I don't know the answer offhand.
Along places like the NEC, many disabled trains are passed by following trains, until a 'rescue train' stops to transfer them aboard, or some other remedy occurs. But in this case it is not the next day's train, just ones minutes or hours behind...