This happened to me once. It's not fun. The threads on either side of the turbo studs are threaded in the same direction - turn right to tighten and turn left to loosen. I first tried using PB Blaster and letting that sit on the fused threads for about 30 minutes at a time. When that didn't work, I tried using some heat. I VERY CAREFULLY heated the area with a propane torch. When that didn't work, I tried drilling a small hole in the center of the stud with a drill and some cutting oil, then used a thread repair kit to try to reverse the broken stud out. When that didn't work, I ended up drilling the stud out with the correct size drill and some cutting oil, then using a tap and die kit to rethread the hole.
My last option was to drill an even bigger hole and fit it with a helicoil. Thank god it didn't go that far. I was prepared to remove the turbo and take it to a machine shop to pay someone to drill it out before fitting a helicoil. Anyway, if I wasn't pressed for time I would have removed the turbo from the engine and put it on a workbench to gain better access to the turbo stud. Leverage is really what you need. Plus, when you drill you must drill as STRAIGHT as possible.
Also, if there is still some threaded part of the stud left that you can put two nuts on it, tighten the two nuts (use regular nuts, not the turbo lock nuts) with separate wrenches against one another and then reverse the bottom nut to force the turbo stud to turn/unscrew counterclockwise.
Good luck.