Update:

I just checked the Michigan statute that the poster was apparently referencing.

It does state that a person has the "right to use deadly force." That is subject to certain conditions and contains limitations, of course. (It is the Castle Doctrine, basically.)

However, "kill the attacker" is not the same as "use deadly force" in my humble opinion. In fact, I suspect one would be in serious difficulty in Michigan...as with most any jurisdiction...if an attacker fled after being the object of deadly force and the "good guy" chopped off his head with an axe after catching him. Yes, the use of the axe is a extreme; I submit you would be in trouble with the law if you shot him then.

Be safe.