Actually, FED rules DO allow you to finish a game with 8 players, IF it is due to an injury. A disqualified (ejected) player is different, though. (My high school team did finish a game with eight back in '99---we had put in all the subs in a game that we were winning by 10 runs, then one of our players was injured while sliding. We had fewer subs than starters, and this injured player was one of the starters that we had not subbed for.)
FED 4-4-1f A game shall be forfeited to the offended team by the umpire when a team: ...is unable to provide nine players to start the game or cannot provide eight players to finish the game...
NOTE 1: An out will be called each time that spot in the batting order comes to bat. If the offensive player must be substituted for after reaching base, the most recent batter not on base is allowed to run for that player.
NOTE 2: A team playing with fewer than nine players may not return to nine players.