You may shoot a fleeing thief or burglar at night but not just a trespasser.
Here's the law and penal code for Texas about shooting the burglar or thief.
Texas Penal Codes 9.41 and 9.42 together define when someone may use deadly force in defense of property (either land, or tangible personal property).
(a) A person in lawful possession of land or tangible, movable property is justified in using force against another when and to the degree the actor reasonably believes the force is immediately necessary to prevent or terminate the other's trespass on the land or unlawful interference with the property.
(b) A person unlawfully dispossessed of land or 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 reenter the land or 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.
However to shoot the fleeing burglar or burglar you must be in reasonable danger as in the fleeing burglar would have to be pulling a gun on you or say something to the effect that they'll be back to harm you.
But if a burglar is fleeing you can keep a gun on them but don't shoot them unless absolutely necessary.
If you do shoot and kill the person then you still might have to go to jail and go through a trial to not be found guilty of murder.
You can't legally just shoot and kill someone on your property just because they are trespassing though and that goes for Texas and other states as well.