Here is what I have done lots of times in the past, if there is a little stub of the broken stud or bolt sticking up. I take the next size nut (for example if the stud is 3/8 I use a 7/16 nut) and place the nut down over the stub, then I weld a puddle into the center of the nut and stub. I am essentially welding a new head onto the stub. This does two things: It gives me something to put a wrench or socket onto, and the heat from the welding generally helps loosen the stud from the rest of the unit. I try to burn it in hot to get it as red as possible.

It also helps to spray some penetrant onto the stud after you weld it and let that soak in for a little bit, but the heat generally does the trick. I also turn the stud just a tad in each direction, progressively going further and further out, feeling if it is easing up a little. This has saved me on countless occasions.

Don