When there is only a short piece of stud left sticking out its best to find a nut that just fits over it and 'burn' the broken stud into the nut (this also works when its slightly below the surface) You have to let things cool down slowly or you make the stud harder and brittle which means it just snaps again.
Heat the case and use some gum remover spray (for freezing chewing gum stuck to carpets)
I have a can of MAXIM CC907, propane/butane mix, gets frosty

Wrap masking tape around 'bolt' head you made ( make a little 'bucket' to hold freeze spray) and the differential expansion frees everything up
Usually works

If not, its out with the carbide drill bits. Never 'lost' a case yet

PJ
Modified at 2.33am
Removed a set of studs earlier tonight.
Wouldn't come loose without some heat, used a small propane torch
I had bought a cheap non-contact thermometer from Harbor Freight a couple of months ago, says it was around 260 deg. F. localised heating around stud but the entire case got quite 'warm'
I also use a Snap-On CG500 stud remover as it doesn't damage threads. It like a collet, gripping full length of thread. Bes stud remover I have ever seen (or used)