The One Ring had the power of turning its possessor into (in effect) a wraith, or at any rate some sort of non-physical being under the complete and direct control of Sauron:
A mortal, Frodo, who keeps one of the Great Rings, does not die, but he does not grow or obtain more life, he merely continues, until at last every minute is a weariness. And if he often uses the Ring to make himself invisible, he fades: he becomes in the end invisible permanently, and walks in the twilight under the eye of the dark power that rules the Rings. Yes, sooner or later—later, if he is strong or well-meaning to begin with, but neither strength nor good purpose will last—sooner or later the dark power will devour him.
(Lord of the Rings, Book I, Chapter 2, "The Shadow of the Past")
This had not happened yet to Gollum primarily because (being in the dark all the time) he didn't have a strong need to use the Ring to become invisible; but it appears from what Gandalf says that it would inevitably have affected him in this way. He would not have died per se, but he would have been consumed by the power of Sauron. Hobbits are unusually resistant to the effects of the ring, but not entirely resistant.
Eventually, then, Gollum would have been entirely overcome by the Ring—this may have taken hundreds more years, but would undoubtedly have happened had Gollum not lost the ring. When it happened, Gollum, being entirely under the control of Sauron, would have brought the ring to him.
Given that Gollum lost the Ring, however, what would happen?
There were in fact goblins who went down to Gollum's lake:
[Gollum] just throttled [goblins] from behind, if they ever came down alone anywhere near the edge of the water, while he was prowling about. They very seldom did, for they had a feeling that something unpleasant was lurking down there, down at the very roots of the mountain. They had come on the lake, when they were tunnelling down long ago, and they found they could go no further; so there their road ended in that direction, and there was no reason to go that way—unless the Great Goblin sent them. Sometimes he took a fancy for fish from the lake, and sometimes neither goblin nor fish came back.
(The Hobbit, Chapter 5, "Riddles In The Dark")
Thus it's entirely possible—even probable, given the Ring's activity—that eventually, one of them would have come upon the ring. At that point, since goblins appear to be effectively under the control of Sauron already, the Ring would make its way to Sauron relatively quickly.