Each copy of Barroom Brawl also includes the opportunity to create a copy, so as long as there are legal targets available and the copies keep successfully resolving, the brawl can continue.

If the opponent to your left chooses to copy Barroom Brawl but not change its targets, both targets will probably be illegal as the copy tries to resolve (at a minimum, both targets would have to survive and switch controllers in response to still be legal targets for the copy), and the player to their left will not be able to copy it.

If both targets are illegal as Barroom Brawl attempts to resolve, it does nothing. No copy will be created.

In a two-player game, the other player is the opponent to your left.

The opponent to your left may choose the creature they control that was part of the original fight as the first target for their copy, even if it would die after the original spell is done resolving. If it does die, however, it will be an illegal target as the copy tries to resolve.

If one target is legal and the other is not legal as Barroom Brawl resolves, neither creature will deal damage. However, the opponent to your left may still choose to copy Barroom Brawl.