But it does fall out, especially if you sections need to be cut it or you have left over bits which you can use rather than buy more. I've used rock wool in a previous project on a single wall construction and if it did not have a layer of osb on either side of the frame, there is no way the insulation would not fall out.
you can staple packing straps, insulation mesh, twine, etc to provide a backing so even with vibration and any settling the insulation will not fall away into the air cavity and remain in full contact with the drywall.
Well, we have demolished our 25 year old studio and there were big gabs in the rockwool from sagging and also from bulking outwards. There were a lot of places in which the rockwool wasn't touching the plasterboard at all. In our new build we have attached fabric with small wood slats to the back of the wall.
The local bigbox home improvement stores around here carry a wire product that's precut to fit 16" on center stud and designed to hold insulation in place. Not sure what it's called, but I'm think it was right around US$10 for a package and I decided to DIY and hold my insulation in with custom cut chunks of acoustic drop ceiling tile instead. This allowed me to make a nice fit and caulk everything to a good seal, but I was later told by the folks at GS that the ceiling tile inside the wall was a waste and I didn't need it.
Like Glen said, anything you can rig up to keep the insulation in place will do.