Two Teams are playing each other with 6-6 records. They hold the last two playoff spots. Both teams have sat all their players this week to force a 0-0 tie. By doing this they will both be in the playoffs and the two teams behind them at 5-7 will now have no shot of making the playoffs. The best these two teams with 5-7 records can finish is 6-7 and that will not be enough to overcome the 6-6-1 records.
Is there a rule against this? Will they be able to sit all their players or will game mechanics force them to start players?
Collusion. And yes that is against Yahoo Rules. Two owners in collusion to manipulate the game to their perceived advantage. I would LOCK their Teams with an Empty Roster and let it stay that way. Or dock them Penaltys (Subtract points) so they both fall out of contention and then let them play with... themselves during the playoffs.
This is against the sportsmanship of the game and violates the fair play of yahoo leagues. However, there is no game mechanics that will force players to starts. The only way to prevent this would be the commissioner editing the rosters for the game. I would recommend him to start the highest projected for each team and let the cards fall where they do.
My guess is that you have a 5-7 records and the commish has a 6-6 record, in which case you are out of luck.