Happened to me twice
Once in Melbourne flying to Tazzie. Changed some money into AUD at a small kiosk with flustered clerk , trying to serve two people at same time she gave us back wrong passports. Flights elft at simialr times but virtually opposite ends of Airport , mine domestic other guy international.
When i explained my suspicions the excellent gate staff rang the currency kiosk who gave them details of the other party -we were ona 717 they were on a 747 so much harder to find the other guy in time. However Qantas accepted my BA Gold Card as ID -to my surpiose and said they would not let the other guys flight leave until they checked everyone. They found him and couriered my passport down to Tazzie. Couldn't ask more than that -or could I.
Some years earlier when I lived in Bermuda I often had to do a day trip to NYC on business. 0700 departure out and 1900 departure back from JFK. Early check in and with Bermudas one car one family rule a long early morning bike (90cc Yamaha!!) ride from my home to Kindley Field young children so a bit of muddle chaos at home at 0500. No passport check at check in since US immigration pre clearance was right behind the desks. Hand in pocket no passport. No chance of getting home and back in time and wasn't a meeting I wanted to miss. However the previous weekend I had played golf with a police sergeant (special branch as far as Bermuda had one) friend and his buddy who was supervisor of Immigration and customs at Bermuda airport. ( i think that was pretty good duty in US immigration service)
So I ask the stern faced lady in her booth if Mr So and so was around and she took a little persuading but she sent a colleague to find out if he was on duty and thankfully he was. I explained the situation and he says no problem wait here. Comes back with an envelope and says open that. Inside all nicely typed is a formal letter explaining (massive exaggeration) that my visit is of significant importance to USA Bermuda relations and I had mislaid my passport but that he was able to vouch for me and requested that I was 'accorded every facility' . And indeed I was very much the VIP when I got back to JFK that evening.
So, ive done it twice- its a horrible panic inducing feeling and I know I have been incredibly lucky on both occasions so I really triple check everything whenever I go anywhere near an airport , Both incidents pre 9-11 and I am pretty sure the same wouldn't be allowed happen today