If you have a violent encounter with a bad guy and he manages to disengage, that encounter is over.
If you chase him down and initiate a second armed encounter while he is trying to get away, it's quite possible that he can claim self-defense if he feels that his life is in danger and therefore shoots you to end the second encounter.That's not remotely true.
Before the stand your ground laws, if you were violently attacked, even if the circumstances of the attack clearly put you in danger of death or serious injury and would normally justify a claim of self-defense, you were still unable to legally claim self-defense unless you could prove to the court's satisfaction that you could not reasonably retreat.
All the stand your ground laws do is say that if you are violently attacked in a place where you have a legal right to be, that you can claim self-defense if the circumstances of the attack would warrant a deadly force response EVEN WITHOUT first proving that you were unable to retreat.
I'm aware of that, and, technically at least, you are correct. But there are some unintentded side effects to that.
First of all, lethal force should always be an absolute last and final option, a last ditch stand after all other avenues have been approached and failed. (Admittedly, you can get to the final option pretty quickly-seconds or less.)
Prior to stand your ground laws, you had a "duty to retreat," a legal obligation to use violence only as a last and desperate resort.
Subsequent to stand your ground, you can pretty much shoot anyone who you believe is a threat (whether they actually are or are not isn't terribly relevant), and it is virtually impossible for anyone to say otherwise because no one can prove what was in your mind at the moment you pulled the trigger. (And let's be honest, that, too, is a result of our "innocent until proven guilty" concepts and our rights to due process of law, which I hold as unassailable.)
So, in my legal layman's view, all stand your ground did was move the lethal option from last to first, and I think
that concept is bad for society overall.