A few notes about this.
1) If someone committed a federal felony, at least on the surface it is clear cut that they could be denied their rights as a natural extension of their conviction. That is, they could be prohibited from having guns or voting while in prison and probation or parole; but this prohibition is just a continuance of their conviction for the rest of their life, like their legally having to identify themselves as a felon for some employment.
2) However, if they committed a state felony, this becomes problematic. It could be argued they could just leave the state to again restore their rights, unless the federal government precluded it as an interstate restriction. But it could also be argued that a felony in one state could be a misdemeanor in another state.
Perhaps an analogy is for a doctor or lawyer who lose their right to practice in one state can move to another state, take the appropriate exam, and practice there.
I would argue that it does not — for if one is to serve one's sentence, then one has paid their debt to the law. To have a perpetual debt (that of firearms, voting, etc) is to assert that the person can never pay that debt and institutes a second class of citizen: one's whose rights have been converted to privileges, granted by the magnanimosity of the state.