When the Nazgûl lose their bodily form, what happens to their rings?

[Mnemosyne]

Originally Posted by Morthoron

I hate to sound heretical, but there is a disconnect there.

Shun the nonbeliever! Shuuuuunnnn!!!

I don't think it's an issue, though. If the Ring had never been found, of course Sauron would have pwned, because all that cutting off the Ring did was delay his victory by a few millennia. The Ring was never necessary to Sauron's victory, just really really useful. He was doing fine in the War of the Ring until his paranoia (because he knew the Ring had been found, and he feared a usurper) got in the way.