This is very anecdotal, and happened many years ago, but I have heard of something like this. A distant cousin of mine was flying with a very inexperienced person to the Far East from Midwest US. They had a layover in LAX. I am not sure of the details, such as the airline(s). Anyway, my cousin's traveling companion had evidently never traveled outside the US before, and forgot that he needed a passport. IIRC, they figured it out when they went to check in for their flight.
What happened is that the airline flew them to LAX and then changed their connecting flight to a day or two later. While in LAX, they went to the passport office and he got a passport.