Surprisingly enough, the relevant State guidance does say that the US will not prevent an individual from renouncing his or her citizenship even if they do not have another allegiance, though it recommends the consular official specifically warn such people of the difficulties of being stateless.

I've only known one truly stateless individual, but he was an Air Force officer in FRY who was in the U.S. on a joint NATO program when the civil war started, so the Pentagon worked with State to give him special status. Not the usual case.