Is there a law anywhere in black and white on paper that says it is against the law to keep a possum that was rescued as pet since if would only die if released into the wild?
There sort of is a law, this one. It does not absolutely forbid owning a possum, but it is required that you have a license to take or keep a wild fur-bearing animal including a possum. There is no existing "license to take and possess as a pet", but you could try under trapping licenses. However, they warn that the
Fur-bearing Propagation Permit does not authorize individuals to possess live fur-bearing animals as pets.This IS NOT a “pet permit.”
Ultimately, what would happen is you apply for a license, but they would deny the application because you don't plan to propagate the animal, or skin it. Although the statute does not specifically prohibit keeping a fur-bearing animal as a pet, it does authorize Parks and Wildlife to promulgate and enforce regulations.
Another approach would be to seek a wild animal rehabilitation permit, pursuant to PWD regulations (here). This is also not a general pet permit, but in case your program of possum rehabilitation fails, you are not required to kill it or release it into the wild to die. There is a test required, to be sure you know how to rehabilitate wild animals, plus a requirement for letters of support from conservationists, veterinarians or rehabilitators.
I wanted to add a piece to @user6726 comment for anyone that comes across this answer which both of you may also find helpful. IANAL so I defer, and your local animal control, authority figure, etc may not be smart enough to know the difference, but...
If you forego the propagation (breeding, I believe) and trapping licenses (there appear to be many others as well), there's this tidbit:
EDIT: This is the same statute listed above by @user6726, and it has quite a bit of info in it. This part of it, specifically, may help..
Specifically, subsection (d) under section 71.005:
Sec. 71.005. LICENSES REQUIRED.
(a) Except as provided by this section and Section 71.004(a), no person may take a fur-bearing animal or a pelt in this state unless the person has acquired and possesses a trapper's license.
(b) Except as provided by commission regulation, no person may purchase, possess after purchase, or transport for commercial purposes a pelt or carcass taken in this state unless the person has acquired and possesses a retail fur buyer's or wholesale fur dealer's license.
(c) No person may capture or possess a live fur-bearing animal for any purpose, except as otherwise authorized by this code, unless he has acquired and possesses a fur-bearing animal propagation license.
(d) A person who possesses a hunting license may take and possess a fur-bearing animal if:
(1) neither the fur-bearing animal nor any part of that animal is taken for the purpose of sale, barter, or exchange; and
(2) the number of fur-bearing animals taken does not exceed the daily bag limit or possession limit set by commission regulation.
also, just to cover the bases regarding 'take' above:
Sec. 71.001. DEFINITIONS. In this subtitle: (8) "Take" means the act of snaring, trapping, shooting, killing, or capturing by any means and includes an attempt to take.
Assuming your locality does not ban wild animals entirely or opossums specifically (or both) to include both city and county, this may be the loophole for the Texas restriction on it being a fur-bearing animal, and as per the statute that regulates them you are able to take and possess them with a hunting license so long as it doesn't violate those stipulations.
I hope that helps anyone searching, but again IANAL.