My favourite example of this was with NHL 98 on the PC (this was before I was working at EA).
I was doing a full 82-game season, 10-minute periods for both the Canucks and Devils. About 2/3 of the way through, I was playing a game and happened to hit the ref through the glass after a whistle. The game hung on the following faceoff because the ref never reappeared to drop the puck.
Instead of just quitting the game outright (this was the 4th straight game I'd played without saving and I didn't want to lose my progress), I went out to the FE and accidentally saved my game in progress. Which meant that my franchise was screwed, as I'd keep going back to that game missing the ref. So I just calmly copied down the relevant info from the stats, standings, etc., simmed a new season to the game I left off, played the rest of the season, added together the stats so the playoff matchups were correct, then started a new playoffs with the correct seeding.
If that happened in 2008 instead of 1998, I probably would've gone to the boards and complained about EA's "gamekilling" bug. Instead I just went about my business.
Hmmm, I had a lot of time on my hands in 1998...