[tropo]

Legal standards vary. In most of the USA, he probably could be shot.

In nearly all of the USA, he could be shot if he were in the victim's home. Most states do not have a duty to flee when in the home, and the attacker's continued presence is considered a threat. Only in Vermont and Washington, D.C. is there a duty to attempt to flee when in the home.

Outside the home, in most states he probably could be shot, at least if he weren't clearly departing. He can't just stay there being a threat. There is no duty for the victim to attempt to flee, even if outside the home.

An interesting case involves a purse snatcher in a Texas parking lot. A bystander pulled out a huge revolver with a laser sight, fired, and killed the purse snatcher to recover the purse. It was legal.