depends on what the shooter saw.
i could see it easily for myself to see a woman get her purse snatched in a dark parkinglot, be struck by the assailant , who then flees. i would give chase. just in my nature. and if a weapon was presented towards me i would not hesitate to fire.
however if i saw a armed robbery and a suspect fleeing. i certainly would not chase. for a purse......now if he had taken a person, a child............i would give chase ready to fire.
really depends on what the shooter percieved to be happening at the given time.
its easy to see a simple crime, try to help and end up in a deadly situation............but the question is........did the shooter know he was armed when he gave chase? if so that is kind of like asking for a violent confrontation.