After Sauron’s defeat at the hands of Elendil and Gil-Galad in the last alliance of Elves and Men, his body was destroyed. It would take him nearly a thousand years to regain power, and over two thousand years to fully reincarnate in Middle-earth. During that time, the Nazgûl retreated to the East, then slowly began filtering back into Middle-earth to cause problems for the Men of Gondor.
But…what happened to the Nine Rings?
Did the Nazgûl miss out on a singular opportunity?
One possibility is that Sauron’s defeat left him unable to “hold” the Nine Rings. At this point, the Nazgûl would regain at least some control over their own wills. Perhaps they could even have sought out and reclaimed the own Rings of Power, breaking Sauron’s hold over them. That Tolkien doesn’t even address this possibility suggests to me that this is not how he imagined it working.
Let’s imagine for a minute that this is how it worked. Does a Nazgûl holding his own Ring regain his full autonomy? Certainly not, so long as Sauron holds the One. However, Sauron does not currently hold the One, and though he is still in ‘rapport’ with it (see Letter 131), he apparently can’t use it to control the bearers of the other Rings (Gandalf, Galadriel, and Elrond all wear their Rings; it’s not entirely clear to me whether the other Sixteen are equally safe to wear). I would argue that the Nazgûl might gain some temporary measure of autonomy, but after having been in thralldom to Sauron for so long, they no longer had any will of their own to regain.
How do you hold something when you’re a cranky, disembodied fart?
A second possibility is that Sauron can still ‘wield’ any Ring he possesses even without a physical body. As support for this theory, note that even after the Akallabêth, where Sauron’s body perished, he was able to use the power of his Ring, which at that point he still possessed. Interestingly, the Ring seems to have survived the destruction of Numenor, suggesting to me either that Sauron didn’t bring it with him (an idea I find unlikely, given its importance) or that it can in some magical way travel with its master even as he is incorporeal. While this is obviously a bit handwavey and not very well explained, I tend to lean toward this explanation. A being not tied to a physical body would surely be loath to pour so much of his strength, power, and spirit into an item fully tied to the physical realm!
Which brings me to another question…
Did Sauron like…rent a storage unit or something?
Sauron had a number of nice things, and I’m not just talking about a fancy throw rug and an IKEA couch. The tower of Barad-dûr was home to several powerful and magical artifacts…not the least of which would be some unknown number of Rings of Power. Are we to believe that when the Last Alliance leveled his tower, they let all that stuff sit there? Or would some of his higher-level lieutenants have run away with all his magical gubbins? We don’t really know, but I have an equally difficult time picturing Sauron picking through the rubble of his tower trying to find several small pieces of jewelry and imagining one of his minions hanging out in a cave somewhere in Mordor with twelve-ish Rings of Power, a palantír, and Sauron’s second-best crown that he wore when he’s just lying around the house.
Although Barad-dûr was leveled, its foundations remained. One possibility is that within the foundations was a vault, and inside that vault lived Sauron’s treasures.
Unsurprisingly, I don’t think anyone really knows the answer
I’ll have to leaf through the Letters to see if Tolkien ever addresses this question, but I suspect it will go unanswered. Some might even go so far as to call the question of how Sauron kept control of his Rings and other goodies while disembodied a plot hole, though of course I would never.