I tried seeing what happens when you kill yourself and then trying joining games through the notification. Well, it seemed to screw up trivia and bowling, so maybe it’d be best to disable or hide those notifications for dead players.
In trivia, I appeared on the trivia screen but I wasn’t playing. When I respawned I could return to the trivia room and see my name on the screen, but other players had to wait for the countdown to end until the next round.
In bowling, I couldn’t do anything and I had to leave the plaza and return to the main menu. However, I could see my name on the screen and my bowling ball was always there on the floor in front of the lane.
I haven’t tested this with other games.