Coming from tournament organising in other games/sports:
1. Never make it bad for a player to tell you he has to leave. He'll leave anyway, he just won't tell you. Super annoying.
2. In elimination play, a player who has to leave loses their next match.
3. In swiss rounds, or other arranged play, re-pair the round as if the player doesn't exist. They keep their match points/whatever, but they don't get any more as time goes on.
4. In a cut-to-finals, if a player doesn't turn up have some rule in effect. Both variants are reasonable (add players until you have the right number/don't) but you should have it in the rules (as both IFPA and PAPA do per bkerins)
5. If a player doesn't tell you they're leaving, feel free to be somewhat more punitive. However, their existing results should continue to exist from a tournament integrity point of view. If I beat you in the quarters and then leave, you don't get to play the semis: otherwise you can have post-match fixing and other Bad Things.
6. Thankfully pinball doesn't have draws.