Legal question: how will the case of "a man bravely chasing a thief and causing his death" be judged if it happens in Hong Kong or European and American countries?

In property crimes, if caught in time, it is possible to recover property. At this point, the pursuit behavior still belongs to the legitimate behavior in criminal law. If it is defined as arrest afterwards, it constitutes the crime of intentional injury. Personally, I disagree with lawyers and lawyers Ye. This is an accident in the process of self-defense and should not be punished.