Contrary to popular belief, that's how most self-defense shootings go. Most thugs are just looking for an easy target, someone who will give in to their demands without putting up a fight, and for good reason, money is no good to a dead man, much less a man who has to spend it all on a trip to the Emergency Room.
The desperate junkies you hear about in headlines who continue attacking after being shot unless thoroughly physically disabled make headlines because such occurrences are extraordinary.

For the average rational human being, the mere sight of a firearm is enough to get them to cease all aggression and flee, the rest will typically surrender after being shot because the sight of their own blood coupled with the searing pain of a hot chunk of lead lodged somewhere inside of their body is enough to make them recognize their own mortality and question whether it is worth it to continue fighting or flee to seek medical attention before they blood out/die.

Furthermore, it's worth noting that in most cases it takes 2 shots on average to down an attacker, regardless of what cartridge the firearm is loaded with.

Not that I'm trying to convince you that you ought to carry a .380 or anything, merely that this story would have most likely ended exactly the same way had the man been hit in the exact same spot with a 9mm Luger or .357 Magnum.