As a result of Haynes v. US, 390 U.S. 85 (1968), a criminal cannot be convicted for failure to register a firearm because to do so would represent a violation of the criminal's Fifth Amendment right against self-incrimination.

To quote the decision...

"...A proper claim of the privilege against self-incrimination provides a full defense to prosecutions either for failure to register under sec. 5841 or for possession of an unregistered firearm under sec. 5851..."