At the end of Frankenstein, Walton describes the monster's last move:
He sprang from the cabin window as he said this, upon the ice raft which lay close to the vessel. He was borne away by the waves and lost in darkness and distance. (24.71)
We don't know for sure that he carries out his intention of burning himself to death, but it seems pretty likely. With Victor gone, the monster has no reason to live—no one left to kill; no one's approval to seek. But then there's the original ending, the one that Shelley published in 1818 before Percy revised it for her. In that ending, it's a little more ambiguous:
He sprung from the cabin window as he said this upon an ice raft that lay close to the vessel & pushing himself off he was carried away by the waves and I soon lost sight of him in the darkness and distance.
What's the difference? There are two: First, the monster "push[es] himself off." In other words, he takes the action. We have the passive "carried away" and "borne away" in both versions, but the earlier one gives the monster some agency. Instead of being a passive victim of fate, he seems more in control of his own destiny.
And then there's the big one: "I soon lost sight of him." It's subtle but important: in 1831, there's no (or very little) question: the monster is "lost in darkness." In 1818, however, Walton loses sight of him. He's still out there somewhere, beyond the reach of human eyes—and maybe just waiting to come back. (Want to read this interpretation with a lot more citations? Check out literary scholar Anne Mellor's book chapter.)