My friends and I played against The Chairman the other day and we ran into a snag. Because Haka had savage mana out and used rampage to defeat all the underbosse’s and thugs, they went underneath, not allowing the allotted amount of underbosses to reach the trash to flip The Chairman. When they defeated The Operative, there were no available targets to be attacked. Does that mean the game ends in a tie, or what is the outcome of the event?
It means you've learned not to do that in the future. Or allow the Unforgiving Wasteland to kill them, either.
Were you fighting in Freedom Tower? If not, then wait until the environment plays a target and use Savage Mana's power to destroy that target, freeing all underbosses and thugs. Or you could use Savage Mana's power to attack a hero, there are a few that can become immune to damage. Another option would be use Ongoing destruction to destroy Savage Mana.
The Chairman is not like Miss Information, he's still a target on his front side, just immune to damage. You could have Savaged Mana-ed and directed the damage at him to get Underbosses in his trash at any point (I would advise waiting until after the last of the Prison break cards has passed!).