Texas State Law and Felon Gun Ownership
Texas Penal Code Sec 46.04 allows, in some cases, for a felon to own a firearm where they reside, but only after five years from the time of their conviction.
Here’s a further breakdown of those rules:
Sec. 46.04. UNLAWFUL POSSESSION OF FIREARM.
(a) A person who has been convicted of a felony commits an offense if he possesses a firearm:
(1) after conviction and before the fifth anniversary of the person’s release from confinement following conviction of the felony or the person’s release from supervision under community supervision, parole, or mandatory supervision, whichever date is later; or
(2) after the period described by Subdivision (1), at any location other than the premises at which the person lives.
The code goes into a lot more depth, and you can read it here.
So, to translate that: it appears that a felon can possess a firearm. But it also appears they have to wait five years after their release from prison or from the time their probation or parole is up.