Texas law seems to say this:
A person is justified in using deadly force against another to pervent the other who is fleeing after committing burglary, robbery, or theft during the nighttime, from escaping with the property and he reasonable believes that the property cannot be recovered by any other means; or, the use of force other than deadly force to protect or recover the property would expose him or another to a substantial risk of death or serious bodily injury.
See this page. Yes, they did spell that “pervent”. Or if you want the official penal code, here. I would need to read the code carefully before leaping to a firm conclusion, but my initial reading tells me that this is a good description of when it is proper to use force, and it looks like a dang good law. I haven’t sorted out the “proportionality” requirements, but a propos this:
does he have the right to pull a previously unnoticed gun and shoot the robber in the back to prevent him from escaping and thus completing his theft
the question is whether a lesser degree of force would be as effective. Perhaps a simple “Stop or I’ll shoot” would suffice. Since the scenario involves armed robbery, considerations of lesser force diminish substantially in moral and legal stature. On the other hand, if you catch a pick-pocket snitching something from your backpack, you’re not justified in blowing his head off. You are justified in threatening to blow his head off so that you can hold him until the police arrive.
In other words, to prevent a person from committing a crime or escaping after committing a crime, you have an unrestricted right to threaten force. If he choses to continue the rights-violation business, you have the right to actually implement force. But the level of force should be objectively justified, thus the fact that a person has violated your rights does not translate into a free execution. Simple drawing your weapon could be sufficient to cause the thief to stop, realizing what the alternative is, and in that case, it would be unjust to start with maximum force. OTOH if the thief has already attempted to kill you, it would be difficult to justify a cautious, persuasive approach. The question which you must answer, as a juror, is whether the particular level of force really was reasonable. The law should punish unreasonably excessive force, but the defendent should be afforded wide latitude in answering the question of whether the force was reasonable. A victim can’t be expected to know that the gun was really a toy gun, or that it wasn’t loaded. The victim can be expected to know that if the thief was the mayor of the city, then even if he escapes, his identity is known and the police can deal with the problem, so it is not necessary to shoot the mayor in the back to prevent him from escaping. (Of course, if the mayor intends to take your property and destroy it out of malice, then you can’t assume that an orderly law-abiding recovery is possible. So the context matters).
[DW: Note that the Texas law does not afford the justification defense in the case of reckless injury or death of an innocent third party, as it should be].