when you are removing dirty rusted or gulded bolts, If you have any movement at all in the bolt there is never any reason for you to brake that bolt off or strip it out. it is only if you get in a big hurry and try to mussel it out that you will have these things happen.
put some penetrating oil on it, start working it back and forth. each time it will go a little further, keep oiling it and soon you will have it. clean the threads and use anti seize compound on assembly.
if a bolt wont brake lose then try tightening it a little first and lots of times it will brake lose if not hit the bolt sharply on the head a couple times and try it again. I cant remember the last time I used a easy out. back in the old days we learned that before we ever got to work on anyone else's car.
to bad they never taught us to spell or type