In backyard cricket, an informal version of normal cricket, you can get "six and out", which means that you score six runs but you're out, if you hit the ball outside of the playing area.
Do any informal versions of baseball have a similar rule?
I've never heard of this existing in any baseball league. However, in some slow pitch softball leagues there are variations of two rules that relate:
xamount of homeruns are hit in a game/inning by a player/team, any further homeruns count as an out.
xamount of runs in an inning/game, or a team may only be leading the other team by
xamount of runs at the end of an inning; and if that total is passed, the inning/game is over.