Some years back we took a villa in Cancun with several other couples, all old friends. One of our friends was late leaving for the airport, and when he reached into the drawer to grab his passport, he picked up an old, expired passport he had unwisely stored in the same drawer. Nobody noticed it on the departure side, but the immigration officer in Cancun spotted it immediately. There was some negotiation, and a few pictures of Andy Jackson were agreed to be an adequate substitute for a current passport.
You can buy anything in Mexico. My husbands uncle died in Mexico of natural causes and the family had to buy his body to get him home for burial.