What happens to firearms you already own if you get convicted of a non-violent felony?
Under FEDERAL law, a person convicted of a felony may not possess a firearm anywhere in the US. You may sell them or give them to someone else, but you may no longer possess them. That means hold, have the keys to the safe where they are stored, carry them, shoot them, etc. If you are found to possess a firearm, that is good for 5 years in a Federal prison, and the guns will be confiscated.
Whether a violent or non-violent felony, once a person is convicted, they are no longer allowed to own a firearm. In Texas, five years after the anniversary of the end of your parole or the end of the your prison sentence, you may possess one in your home; however, you may not carry one with you outside.