Stone Age ought to be abandoned. Not only are there slight rule changes with less players, but there's a problem with one person going first two rounds in a row. (It still has the player who is gone go first, which of course just dumps it to the next player, who then gets to go first again on the next round.) I imagine that same problem exists in any game that does a ABC, BCA, CAB turn order.
Can't Stop continues. Perudo seems not to. I believe Yahtzee stops IIRC.
I don't know that anyone knows how every single game works. I think all games should require the players to state if they'd like to continue after a player leaves - make that their next turn. If any one person doesn't want to continue, it shouldn't - that's not the game they agreed to. If everyone wants to continue, that's certainly fine. There's no ELO and everyone needs to know that. (Some people won't care, but others might.) This ought to be default for all but a very few games. While we can suggest a group abandonment, when it's turn based, people don't always see that cause it's not their turn.