I am sure many folk have done it without problem, and in fact I have myself. I have also run into problems, however, so I tend to be cautious. The insulation on one cable dried out and cracked, leading to shorted wires under the carpet and a mess to replace, and in another case best I could tell the conductors were simply pulled apart by traffic (the wires crossed at about a 45 degree angle). May have been bad wire. Thinking back over the years (decades, whatever), I cannot recall doing many installs under carpet, probably only a handful out of the few hundred installs I worked (a paltry number for somebody doing it as a living, but I only did it a few years and installation was never my main job). I know I have seen scuffed cables and such, but honestly I can only remember the two failures; maybe they just stand out.
Another issue is that a lot of the work was commercial, and Code said no wires under carpet. May not have applied to audio cables, but we treated them the same as all other wires. I know we would get hasseled by inspectors if we ran wires across a walkway even in those protective runners.
So, given the knowledge base of Wayne and Arny, I concede this one to their superior experience. I still wouldn't do it, but that's the way I was weaned.
I agree with Wayne that if the sub cable is line level, go for standard shielded.
"After silence, that which best expresses the inexpressible, is music" - Aldous Huxley