He thinks it'll be his guardian angel that will save him, but the guardian angel is really a monster, so Jake is the one he assumes
he and Jake are able to get out together, but it ends up where Princess Bubblegum saves both of them!
He expected Jake to save but his supposed "Guardian Angel" saves him but really didn't, it wanted to eat him. He expected Jake to save him but he to was in the cage, tho in a way it way Jake it did save them (at least for the time being), but it was Princess Bubblegum who really saved them, riding in on her swan, she saves them from their own stupidity and gets them out of the dungeon all together.
This is a tricky question... But since the first part of the question says "save" in quotations, I would think that means he expected the Guardian Angel to save him (since that didn't turn out to be the case).
However, after the Guardian Angel says the secret to cooking him is a low flame over a long period, Finn says that's Jake's secret too. Then he says "Sure hope he saves me." So he does pretty much flat out say he expects Jake to save him. However, I'm taking "save" in quotations as a hint that the Guardian Angel is the answer.
And of course, the answer to the second part of the question is Princess Bubblegum saves him (and Jake) in the end.
TL;DR: He expects the Guardian Angel to "save" him, and Princess Bubblegum actually does, in the end.
He expects Jake to save him at first.
Then his guardian angel shows, and he expects his angel to save him, which dosent happen.
Jake goes to save him and they obtain the crystal eye, thats when princess bubblegum shows up and saves them both.
This is a tricky question. First he expects that his guardian angel will save him, but then the guardian angel mentions cooking him. Jake does his best to save him, but in the end Bubblegum rescues them both.