To center a drill on a ragged broken stud I machine a drill guide for a center drill. The drill guide should fit snugly in the hole and the end of the guide is as close to the stud as possible. Once the center hole is drilled I use a LH drill to drill through the drill guide and drill out the bolt as close to the minimum diameter as I can, then use a Proto 4-sided extractor to back it out. This, plus a lot of lube, usually works.
The Mig technique works well, especially if the stud is sticking out of the work.
The Mig technique works well, especially if the stud is sticking out of the work.