If there's no referee, it's up to the players to agree to a stalemate. There are two options:
- Both agree that it's a possible stalemate, in which case you each play 3 more shots. If no progress is made, a stalemate is reached and the game is to be replayed with the original breaker of the rack breaking again. If this is the option you decide upon, you should note:
- If any progress is made (object balls moving, players fouling, balls pocketed, etc), the game would continue as normal.
- If during those three innings any player fouls, those fouls would be assessed according the applicable rules (which could result in one player losing/winning the game).
- Both agree that it's a certain stalemate, in which case the game is to be replayed with the original breaker of the rack breaking again.
But, without seeing a photo or diagram of exactly how the balls are resting, it's very hard to tell if there is any plausible chance for progress or not.
Are you 100% sure that the opponent (shooting at the two object balls blocking the 8 ball) would have no chance of tapping one of their balls loose (e.g. from the side)? You have to think about it like this—could a very skilled player do it legally? If so, that player should shoot, and depending on whether the 8 ball falls into the pocket or not, either lose the game, take a foul (if no balls touch a rail), etc.
Here are the World Pool-Billiard Association's "Stalemate" definition from the "General Rules" section (which is not specific to any particular game):
It tells us that in general, a referee would allow each player to have three more turns at the table and would only declare a stalemate if there is still no progress (or if both players agree, they can skip the "3 turns at the table" and go directly to a stalemate outcome.
1.12 - Stalemate
If the referee observes that no progress is being made towards a conclusion, he will announce his decision, and each player will have three more turns at the table. Then, if the referee determines that there is still no progress, he will declare a stalemate. If both players agree, they may accept the stalemate without taking their three additional turns. The procedure for a stalemate is specified under the rules for each game.
Then, the WPA 8 Ball rules further specify what happens in the case of an eight ball stalemate in section #3.11 - "Stalemate". It tells us that, in the event of a stalemate in 8 ball pool, the original breaker of the rack will break again in the rematch.
3.11 - Stalemate
If a stalemate occurs (see 1.12 Stalemate), the original breaker of the rack will break again.
So, when players believe they may be in a stalemate situation in 8 ball, they should either:
- agree to stalemate and replay the game, or
- each take three more attempts (where either one player will win or lose, or no progress is made and an automatic stalemate is applied and the game replayed).
But again, without seeing a photo or diagram of exactly how the balls are resting, it's very hard to tell if there is any plausible chance for progress or not.
Since bar room rules vary from place to place, players might decide on a re-spotting of the object balls (or at least the eight ball), to a neutral area. It might also depend on whether you are playing on a coin-op table for the bar question as many of the rules relating to the 8 ball get "adjusted" when playing in a bar on a coin-op pool table.
It will be interesting to hear what has to be said on this one. It's a good question though. It is a real thinker, and does not come up very often.