Have you ever de-boarded a plane of your own volition?
Two years ago, I had a flight on Christmas Eve from LGA - ATL - CMH, where my parents live, on AirTran. I already knew I'd have a tight connection in ATL (35 minutes). I actually arrived at LGA well over 2 hours early and tried to get on an earlier flight because of my concerns but no luck.
Then, we boarded the flight more or less on time, but were stuck at the gate for a good 15-20 minutes because we were waiting on a member of the crew or something. Feeling even less certain about my chances of a good connection, I finally asked a roaming FA if I could get off. The next ATL - CMH flight on AirTran didn't leave until around 1 PM on Christmas Day and I did not want to spend Christmas in the Atlanta airport (I'd rather spend the night in NY if I had to). So even though I was in a window seat, I got out, took my carry-on bag from the overhead bin, and left, amid numerous comments of "good luck" from nearby passengers.
Before I got on the plane originally, I did happen to notice that a nonstop flight to CAK (about 2 hours from CMH) was set to depart about an hour after our ATL flight. So I started to walk over to that gate. The GA at the ATL flight ran after me and asked what my name was, assumedly to "un-board" me. An extremely happy standby passenger was then let on. So I got to the CAK flight and explained my situation. The GA there called customer service and was able to get me on the flight, which he told me had one open seat. My dad then picked me up from CAK and we had a long ride to his house, but I made it in time for Christmas.
I never did look back to see what time my the ATL flight arrived and when the CMH flight took off...