In the original universe, we've seen Finn's father, Martin in the episode "Escape from the Citadel". He then escaped to space, but he might have a chance of being still alive.
If you're looking for Farmworld Universe, Finn's father (Mr. Mertens) ran away with his family after Ice Finn told them to do so. Not sure if he's still alive.
Then after Jake's wish (In "Jake the Dog"), that universe was probably somehow altered. So who knows?
Yes as we saw in "Escape the Citadel" he went off into space. But in "The Tower" we thought Finn's father was in the tower but it was just PB in disguise. So I'm not very sure if Martin is alive or not only time will tell.