Reading Haynes vs. U.S. more closely, I realized that it has nothing to do with the defendant being a convicted felon (I don’t think he was!). It simply observes that, given the way 26 USC was formulated in 1968, the only people who might be required to file registration forms for their firearms, with rare exceptions, were those who obtained their weapons illegally.
In principle, the Fifth Amendment privilege is not an absolute protection against providing information to the government. For example, income from selling illegal drugs in taxable and you can’t hide behind the Fifth Amendment to refuse filing taxes. (See United States v. Sullivan, 274 U. S. 259; Shapiro v. United States, 335 U. S. 1).
The decision in Haynes vs. U.S. remained relevant for about nine months, because, in October 1968, the Congress passed an amendment to the National Firearms Act, intended to cure this specific problem:
[quote]Title II of the Gun Control Act (GCA) of 1968
Title II amended the NFA to cure the constitutional flaw pointed out in Haynes. First, the requirement for possessors of unregistered firearms to register was removed. Indeed, under the amended law, there is no mechanism for a possessor to register an unregistered NFA firearm already possessed by the person. Second, a provision was added to the law prohibiting the use of any information from an NFA application or registration as evidence against the person in a criminal proceeding with respect to a violation of law occurring prior to or concurrently with the filing of the application or registration. In 1971, the Supreme Court reexamined the NFA in the Freed case and found that the 1968 amendments cured the constitutional defect in the original NFA.[/quote]