I guess I'm missing how the loop is formed.
A machine will in most cases have the chassis connected to power ground, if not, it may be bolted to somthing grounded (a machine that I was told was NOT grounded was water cooled by copper pipes :).

Some conductivity from the machine to ground usually exist, most often a good one.

Now you connect - as you should - your device to ground. So we have ground to ground and your shield forming a beautiful loop.

That loop will exist even if you use a solid wire, so why not the shield? Well, if there is noise between ground and ground that will be distributed across the cable rather than shielded against. I once had to use shielded wire with the ground wire outside the shield.

If all things are in wooden or plastic cabinets and are not connected to ground - maybe - you can connect both ends of the shield (as in audio).

I have been told by authorities in the field not to ground both ends - I know that there are some that argue that you should. However even those will tell you to use a wire as ground, not just the shield (why they then insist that both ends of the shield must be connected, I do not know)

Anyhow, it is simple to try, why don't you.

Erik