I take Formendacil's stance, that Sauron kept the Nine Rings so he could control the Nazgul, even without the one. A rather older thread done by Kransha (
here is the link ) goes into what if Frodo claimed the ring? And was able to wrest power from Sauron, becoming the new "Ring-lord." Tolkien addresses this answer in
Letter #243. That eventhough Sauron was not in possession of the one, he was still able to control the Nazgul. The Nazgul were enslaved to their Nine Rings, and Sauron kept them so he could control them, even without the One.