Absent a local league rule, ASA's shorthanded rule (4-1D) comes into effect whenever you play a FP game with less than 9 players. If you start with 8, the 9th spot is left open and an out is recorded each time it comes up.For us (10U ASA), the lineup at the start of the game is the determining factor, not the full-season roster of the whole team. If we turn in a lineup card of 8 players before the game, then we are expected to bat 8 players for that game. The only way there's a out for a missed AB is if one of those 8 misses her turn.When a team is playing short-handed, they have to take an out whenever the empty spot come up in the line-up.
Our LL baseball allowed teams to bring up players if a team knew they were going to be shorthanded. I don't recall it being allowed at our local ASA league, only some games being rescheduled because one or both teams wouldn't have enough players.