The Power of Isengard

[Boromir88]

Eomer, sounds like you are looking for an answer that Tolkien wrote in a letter to Mr. Milton Waldman...

While he (Sauron) wore it, his power won earth was actually enhanced. But even if he did not wear it, that power existed and was in "rapport" with himself: he was not "diminished." Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge Sauron, become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place.

So, we have the Ring's power is still "rapport" or "bound" to Sauron. However, if someone comes along (say Gandalf) and is strong enough to challenge him with it (one on one) and is able to beat him that bond would be broken. The Ring's powers would no longer be bound to Sauron, therefor he would be destroyed for good. However, as SpM says, Sauron's works would live on, as the new Ring-Bearer would turn up to be a new dark lord. If you're still confused check out this thread