The nut can be cut with a chisel and/or dremel (especially with an air chisel with a wide variety of small bits to choose from), the bolt can be drilled with a special center-alignment drill, an extra nut can be welded on the bolt head for extra grip. Just to give you examples, the actual solution can be made only then and there. Not every shop mech is good at these things, the guys who actually fabricate and restore metal parts can do it. An average bolt-on-bolt-off shop would not even have old school tools like wide variety chisel set and counterclockwise drill bits with centering aid but a shop with a lathe and furnace can do anything from anything.
All this and if you're lucky, you can continue soaking it and maybe it will eventually come loose under its own power so to say, without having to cut or drill anything. But if it has to be cut or drilled then it has, for an experienced metal worker with all the right tools it will not make difference how and when you shear or strip it.
Oh and another tip. Put a pressure on the bolt (counterclockwise torque that is) and tap the nut with a small hammer, using a punch if necessary to gain access. Simulates the air wrench which uses vibration to open up interlocked threads. This may need four hands to do it really effectively.
As it is a nut and bolt setup, these parts are sacrificial, one would have to be much more careful when a thread inside of a block or case is involved. But it is a special lock nut with this sheet-metal locking thingy behind it so if I was doing it, I would perhaps even try to save the nut just as if it was a precious inner thread. That means drilling the bolt dead center and all that.