[Keeper of Dol Guldur]

Since Frodo saw rings on the hands of the Nazgul when he was in their realm of ethereal appearance, I would maintain that the rings themselves phased out of physical reality along with the wraithes themselves. The jewelry likely was what kept them in that state of not-being.

I think the question would be, when the Witch-King was destroyed, did his ring magically zap back to Sauron, and if then could Sauron do it again? And I'd have to say a resounding no. By severing the Witch-King's magical sinews, Merry and Eowyn seemed to have also severed his spirits link with the physical realm (it may not have existed there, but it had a link, and that's why it could be clothed in the garb of the Ringwraith), and so the ring would in turn be trapped, severed from the material world along with him.