Various states addressed this issue many decades past.
FWIW, if you read the Federalist and Anti-Federalist Papers, you find that both sides agreed that "felons, the insane, and persons of ill-repute" (or words to that effect) should not be allowed to bear arms. As near as I can tell, it was assumed by the writers of our Constitution that the state governments would deal with this issue.
In Texas, a non-federal felon may have guns in his home, but not outside the home. He can't hunt nor target-shoot, but he can defend himself in his home.
FWIW, Art