Cables made with TSP (Twisted Shielded Pair) wire, include a high and low signal conductor, so the shield is separate and ought to be (and is) grounded at one end only. I use such directional wires as intended with the arrow pointing away from the signal source, but I can't say that I detect any difference the other way around. It probably depends on whether your rig has grounding problems that the shield can help with.
However, all the talk about "noise floor" in connection with this subject, and many others, is a bit academic IMHO. On every recording that I own (even LP's with surface noise) I can always tell when the recording begins (just before the music starts) from the background noise that is in the recorded program. My system's noise is significantly lower than the typical recording, so I do not consider it to be a problem needing fixing.
