For advice on whether you can legally possess a firearm while living with someone who has been convicted of a felony, it is best to consult with an attorney who can evaluate your specific situation and provide you with advice on how to comply with the law.
See our FAQ "Can someone who has been convicted of a felony own a gun?" and the Felons & Firearms page of our Gun Laws research guide for information about the laws that prohibit firearm possession after a felony conviction. Unfortunately, Texas and Federal statutes do not provide a clear definition of exactly what “possession” means. For this reason, if a person is charged with unlawfully possessing a firearm, the court will likely need to consider many different factors to determine if the person was truly in "possession" of the firearm.
One legal concept that may come into play is the concept of “constructive possession." This concept means that even if a person was not in direct control of something, if they knew it was there and had the ability to control it, it may qualify as legal possession of the object. For example, if your spouse knows that you keep your firearm in a safe and they know the combination to that safe, a court may find that your spouse legally has possession of that firearm. This article from a law firm explains the concept in more detail.
Many factors may come into play when answering this question, and constructive possession is just one example. For advice on whether you can legally possess a firearm while living with someone who has been convicted of a felony, please consult with an attorney.