Another way I have have success with.
Drill a hole the size of the rod you use in a stick welder in a piece of wood. Clamp that over the stud to be removed so you don't miss. Intentionally make the rod stick to the broken stud and in the process the current going from the stud to the block blows out the rust. After it cools the rod may turn out the stud.
Had a 1/4" bolt broke off deep in a blind hole. Used a piece of 3/16" steel brake line with a insulated tube they use in electric motors to insulate the wires inside the tube to insulate a Mig wire from the tubing. Glued it in leaving 1/16" of the tube exposed in the bottom of the hole. Fed the Mig wire down the tube and was able to weld the steel tube to the bolt enough to turn it out with my fingers. I know the bolt was seized because I broke it off trying to remove it.
Edited by GWest, February 25, 2016 - 05:22 AM.