I never heard of a drain wire! Maybe that's why my discipline was process / mechanical.

A shield provides for protecting what's inside of the shield from coupling with signals that are outside of the
shield. Likewise it keeps signals inside the shield from being getting outside of it. If the shield was a continous metal tube
one would say that there is 100% shielding. The shield can provide a least resistive path to earth ground. You don't send the signals traveling outside the shield to another circuit connection as that would be just coupling the interferjng signals
to some other circuit. Now what hapens inside is a different story. If an offending signal, noise ( noise is not understood by us), is inside of the shield then it can couple and get mixed in with the signal on the wires. The uninsulated wire can offer
a less restrictive path to ground and help minimise the the noise. So guess one could say it is "drain for the conduit" ie; the conduit is filled with liquid and want to get rid of it...............
Yes leave the one end unconnected.
Noise can be a real bear to find and get rid off or control, but, a seperate ground system for noise is the first step to elimination.
As the saying goes is the above "clear as mud"?

RICH