They did escape, in the older tantrum v3 they would've had died but it was changed so that Bert and Ernie runs, big bird only stays there because corruption grabs his leg, it's also Confirmed that Bert and Ernie escape, there's even a cut scene showing Bert and Ernie running away (sorry if I sound like a nerd I've been watching pibby ever since that Trailer made by adult swim made)