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Few choices:
1. If your careful with a grinder and cutting wheel you can cut it off
2. Cut the stud off and just replace it
3. Torch the nut/stud off
4. Go to any parts store and find a 12 point socket that fits it well over the nut. Pound it on if you have to then take a breaker bar or a big ratchet and get it off. If your lucky and can find a bumper with a hole for a hitch ball in it, take the socket, a decent punch and a small sledge and you can pop the busted nut out. Then take the socket back or keep it.
5. Sears and similar makes bolt offs which will remove damaged nuts
6. Nut splitter from sears.
If you put a 4 way lug wrench on it, and pull up or down on the bar at the very end, you might be able to snap it off. I did this on a car by-accident once when I wasn't paying attention to what I was doing. Not sure if it would work on a 1/2" stud though. Then replace the broken stud. They do make sockets for stripped nuts, which have gotten me out of a jam a couple times.
If you heat the stud or around the stud DON'T forget to let air out of the tire, or you could get a big BOOM, But like mentioned before weld another nut to it, then remove, either way replace the stud, any heat will weaken it.