These are the Texas Penal Code Provsions on the use of force in protecting property. I've left out the parts that have nothing to do with someone fleeing.
Sec. 9.41. PROTECTION OF ONE'S OWN PROPERTY.
(a) * * *
(b) A person unlawfully dispossessed of . . . tangible, movable property by another is justified in using force against the other when and to the degree the actor reasonably believes the force is immediately necessary to . . . recover the property if the actor uses the force immediately or in fresh pursuit after the dispossession and:
(1) the actor reasonably believes the other had no claim of right when he dispossessed the actor; or
(2) the other accomplished the dispossession by using force, threat, or fraud against the actor.
Sec. 9.42. DEADLY FORCE TO PROTECT PROPERTY. A person is justified in using deadly force against another to protect . . . tangible, movable property:
(1) if he would be justified in using force against the other under Section 9.41; and
(2) when and to the degree he reasonably believes the deadly force is immediately necessary:
(A) * * * or
(B) to prevent the other who is fleeing immediately after committing burglary, robbery, aggravated robbery, or theft during the nighttime from escaping with the property; and
(3) he reasonably believes that:
(A) the land or property cannot be protected or recovered by any other means; or
(B) the use of force other than deadly force to protect or recover the land or property would expose the actor or another to a substantial risk of death or serious bodily injury.
I don't know if the phrase "during the nighttime" applies to "burglary, robbery, aggravated robbery, or theft" or just theft. If you are doing contingency planning, I'd ask a lawyer first.
I'm not going to shoot someone running away with my TV at night. I'll just hope they trip on some of the tools scattered in the front yard and get hurt.
It would have to be something that represented a very large portion of my material or emotional life before I shot someone like that. I can't even imagine what those things would be.