I’m guessing that in most jurisdictions in the USA, even former felons can have some type of defensive weapons or tools, at least at home (the laws about carrying weapons on the street are a lot stricter, and more common across the USA). Not guns– not if the person has been convicted of any felony or even a “family violence ” or “domestic violence” misdemeanor. And nobody who is currently on parole or probation (felony probation) can have any sort of weapon either.
But for a person whose sentence has been fully completed and is not under any kind of supervision, I think most states do allow some sort of weapons for home defense.
Here in Georgia, any firearm is off-limits, but edged weapons and impact weapons would be legal, generally. So would all the “non lethal” alternatives like tasers, stun guns, chemical sprays like MACE, OC, pepperspray, etc. Our law against felons in possession of guns applies to firearms only (including black powder and muzzle-loaders) and some sort of space weapon the legislature envisioned 50 years ago– something that propels a bullet through an electrical charge (Gauss gun? Mag-lev rail gun???)