Texas law says no, but it contains an exception. Section 46.04 of the Texas Penal Code makes it illegal for someone convicted of a felony to possess a firearm.Whether Federal or State Law prohibits the sale or disposition of a firearm to you. Certain violations of the Gun Control Act, 18 U.S.C. § 921 et. seq. How Firearms Background Checks Work. When someone tries to buy a firearm, the seller—known as a Federal Firearms Licensee (FFL)—contacts the FBI. Our laws contain notable gaps that allow individuals who have demonstrated a significant risk of violence to possess firearms. One group of people who are likely to see their firearm rights dramatically impacted are convicted felons. Under the Texas Penal Code, false imprisonment falls under the statutory offense of "unlawful restraint. Prohibit anyone convicted of a felony and anyone subject to a domestic violence protective order from possessing a firearm.