Without going into a Texas law research project - many states allow deadly force to prevent any felony involving the use of force - here, for example, you can kill a purse snatcher who is unarmed.
I don't necessarily agree with this. While I don't research every use of force statute from every state, I find it hard to believe that many states allow you to use deadly force involving a felony where force is used by the suspect. A purse snatcher is normally not going to subject someone to serious bodily injury or death. So how can you justify using deadly force against him?
If I'm pursuing a purse snatching suspect and fire on him I'd be looking for a new job and possibly a lien on my home. And I have greater protection as a LEO.