Sauron with the Seven (three recovered) & the Nine

[Inziladun]

Originally Posted by Alfirin

It's nowhere in the canon, but I've alawys imagined that by the third age the Wrath and his ring were in all respects the same thing, that, if you could destroy a wraiths ring you would instatly destroy the wraith much as with the one ring. I als think this might have worked the other way in the case of a wraith, if you destroyed the wraith permanently his ring is destroyed as well. I have an image in my mind of Sauron at the Moment Eowyn slew the WK looking down at his hand the the WK's ring cracking and falling to pieces.

I'd say the Ringwraiths indeed would die if the Nine that enslaved them were destroyed. After all, it was the power of those rings, and their link to the One, that kept the wraiths walking the earth long after they should have died. But the rings themselves would not have been so tied to their 'masters'. They were under the power of Sauron and the One, and would have endured as long as he and it did.