Ocasionally for tight areas you can get a smaller nut splitter. It does exactly what the name implies. There is a chisel held in a loop. When you tighten the bolt on the chisel it splits the nut. Usually does not damage the bolt at all. When the nut splits there is very little or almost no tension left on the threads. Thats because the nut is made larger by the forced split.
Or perhaps you could drill into the side of the remains of the nut. Probably damage the bolt though. Wear safety glasses if you are doing something like that. You might even manage to cut it off with a dremel type tool. Others may have more creative ideals.