Nope, if you hunt someone down after they are no longer a threat that is murder even in Texas and you do not have absolute right to kill to protect property even in Texas. The use of lethal force in defense of even property in Texas is not absolute. Don’t believe me set up a trap that will kill a thief and if it goes off and you are not at the property when it goes off you will indeed enjoy free room and board from the state of Texas.
Always told to drag’em back on the front porch.