Jeff's reply in Why didn't Voldemort use the Unbreakable Vow with his Death Eaters? naturally brought up the question of what would happen if Voldemort entered into an Unbreakable Vow and then broke it? Breaking the vow would require him to die but the Horcruxes should protect him.
The Dark Lord would likely be ripped from his body, but not die.
The Dark Lord was tied to life by his Horcruxes - as long as one or more of his Horcruxes remained intact, his soul would remain tied to earth and alive in spirit form even if his body died.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
The Dark Lord can survive things that would usually be deadly, he’ll be ripped from his body instead. The rebounding Killing Curse also would have killed him if his Horcruxes hadn’t tied his soul to life - but because of his Horcruxes he survived it in spirit form.
“I was ripped from my body, I was less than spirit, less than the meanest ghost … but still, I was alive. What I was, even I do not know … I, who have gone further than anybody along the path that leads to immortality. You know my goal – to conquer death. And now, I was tested, and it appeared that one or more of my experiments had worked … for I had not been killed, though the curse should have done it.”
- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)
Though it’s unclear exactly how someone dies after breaking an Unbreakable Vow, it’s unlikely it’s any way that’s sufficiently powerful to force the Dark Lord’s soul ‘on’ when a Killing Curse couldn’t.