[Kalimac]

I can't honestly see Gollum wanting to live even a minute after the Ring had perished; unfortunately it's hard to picture him being sad but relieved, because it's impossible to visualize a Gollum who doesn't have the Ring as the core of his existence. The Ring has basically taken the place of Gollum's heart; it's as precious to him as a normal person's heart is to him, and has become just as impossible to live without (though obviously it doesn't need to be physically present for Gollum, it just needs to exist). But once the Ring was melting down in the fire it would be as if his heart had been destroyed - he probably wouldn't have any thoughts whatsoever except that he had to be faithful to the Ring to the end - hence, casting himself into the fire. And he'd probably get pretty murderous if Frodo or Sam tried to stop him. (Not, unfortunately, that I can picture Sam trying *that* hard).