they do make over sized splined lug studs to repair this. most of the time you get luckey and the stud pushed back out of the hub and thats why it spins.
as for getting it out there are two things that have worked well for me depending on how bad it is. first you need to get some PB blaster or the like on the threads, if its not an open ended lug nut drill a hole in the end. the chrome is real thin so it won't be a problem then soak it with PB.
now the two ways to try are either take all the other lug nut off and then get a pry bar behind the wheel to put pressure to hold the stud in the hub. you can also get a socket, punch or prybar between the rotor and wheel then tighten the 2 lug nuts opposit the bad one to pull out on the stud then try and get it off with an impact.