Soft crumbling walls, electrical mounting box
At this point, I don't think an old-work box can be used. As bib mentions, you need a sturdy surface to attach these. You also have a plaster repair in your future, so if you're going to patch that, you may as well go with a new-work box. You have two styles to chose from, one with a tab that attaches to the face of the stud and another that nails into the stud:




I'd recommend the version that nails into the side of the stud, but I'd also recommend swapping out the nails for screws. The process of nailing this box in will disturb a lot more of the plaster.

Go ahead and open the wall up enough to install the new-work box, get the cables inside, screw it to the stud, and secure the wiring with staples to the center of the stud. Then patch your plaster by installing some backing material, applying the plaster with a wide knife, and smoothing the joints so they can't be seen with a light shining at a sharp angle.