An author writes 99% of a book, and then never finishes it and won't give away the ending.* The hero is at the figurative precipice facing certain death, but the character's end is never written and the reader can never find out the true ending. Is the character dead?
No, yes, maybe, neither — because this isn't a meaningful question to ask about a character in an unfinished story. Does the character die? We don't know — the ending doesn't exist to tell us. Is the character dead? Well no, because they didn't have the chance to die or live.
The character is in literary limbo, neither alive nor dead. Which is to be expected, since as soon as the norms of the medium are broken — the story unfinished, the campaign climax unplayed — you are no longer relating to them as a person in a living fictional world, and have begun relating to them as a broken fragment of an unfinished make-believe exercise.
Does it even matter if he's alive or dead in that campaign? Not practically, no. You have the character, so do whatever you want with it.
The character is whatever you want them to be. Nobody can take them away from you, so you can finish their story however you would like to finish it, in the privacy of your own head or your personal fanfiction writing, or even, yes, as a character in some other DM's campaign.
Go for it! Take that character sheet and find a DM who's cool with transferring the PC to their campaign.
They're not even dead, they're extra-dead. When the universe that sustained their personal reality stopped existing they stopped existing with it.
Looked at alternatively, the character in isolation isn't what compels us during an RPG, it's the character in motion and in the context of the unfolding plot, which gave them their initial reason to exist, that compels us. Not only that, but in the context of an RPG our character's existence is validated by the collective belief in them granted by those other players and the GM. You could imagine him alive, or take the character sheet or even just concept to another game and play him again, or finish off his story in your own head, but it doesn't feel the same, does it? The character that lived and breathed in that world that was made up of your shared imaginings can't continue in it, can no longer receive the collective blessing of those who validated his existence for so long, and so he might as well be dead.
It's up to you. As good as dead, because the campaign died? Sure. Still alive in your own mind or a different DM's campaign, cloned into a different imagined reality that still exists? Sure, that's true too.
The point is that however you feel about it, is how you feel. Whatever you do with the character in the future is what you do. Questions about living or dead don't really apply to a character once their fictional context becomes invalid by stuff happening in the real world, so you just have to do what you're going to do.
* Can you imagine the hate-mail that author would get?