[Celebuial]

I agree partly with Mormegil, but I don't think Gollum or I suppose Smeagol (seeing as The Ring is gone), would've perished. Sauron, put some of his 'life force' into The Ring when it was created, thus binding his fate to that of The Ring. Gollum however, had 'an addiction' to The Ring, and although his fate was undoubtably tied up with the fate of The Ring in general, I find it hard to believe that he would be destroyed if The Ring was. Part of him, Gollum may have been destroyed, but I think it more likely that he would hang around to torment him until he died a long, long time later: Smeagol didn't willingly give all of himself up to The Ring; a small part of him resisted. Frodo, although he was in possession of The Ring for a much shorter time span, was permanently tormented by the thought of The Ring, even after its destruction. Maybe this suggests that Sauron's spirit was somehow reaching out to him from The Void, or maybe Eru never meant for such creatures to take such torment, and his mind was permanently scared. I don't think that part of Frodo was destroyed though, just that he saw the world differently, and had endured too much.