I was playing the digital game today and had something new happen which I had never really thought about before. If you knock out the Chairman before the Operative, he goes into the Villain trash and can come back into play if the Villain trash is reshuffled.
At first I thought this was an error, but then I realized that since The Chairman's card doesn't say to remove it from the game the way Omnitron's does, then the only other correct choice is to put it in the trash and, therefore it's eligible to come back into play if it got to the top of the deck.
Normally, this isn't an issue becuase by the time I've taken out the Chairman I'm usually about to win; but once I noticed it, I had to play it out and see if it would indeed happen. It took some doing (using Savage Mana to trap almost every other target in the deck), because when only the Operative left, she'll resuffle the villain deck each turn, so I left the Informants out and used dual Infrared Goggles to speed things up, and yes, The Chairman re-entered play back up to his full HP.
Of course, I have no idea how you'd do this if you were using the Oversized Villain cards :-)