I found out one of the studs holding the exhaust to the jug is stripped by it's former owner. Any idea how to remove the stud on an '05 H-D 1200 ROADSTER?
Holding the exhaust to the jug? Do you mean to the cylinder head? Weld a nut to it and crank it out. Piece of cake unless the stud breaks. Even if that happens it's not that big a job to pull the head and drill it out. Good luck with it and welcome to the forum.
Yes. Weld a nut on. Make sure you unscrew the welded nut as soon as you put down your welding rod while everything is still hot. I've seen this done at places I've worked before and the stud should come right out.