Playing with 8 players

Under OBR this is not allowed at all.
When a team is unable or refuses to field 9 players the game is forfeited.

Under Fed Rules it is permissible to continue the game with 8 players. The team takes an out each time that position in the batting order comes up. The team can not, however, return to 9 players later if more players show up.

I feel that I should add, though, that some summer leagues will allow a player to be added in later if the player who left the game went out due to injury, illness or other just cause.
Most won't allow a later replacement if the player was ejected for an unsportsmanlike act.

it is permissible for the late player to enter the game as a sub, but the team must continue to only use 8 players on offense and defense.