It's a "conductor" and you need to do what is best for the install and what is to be shielded. For a VFD you "connect" both ends, since it is a return conductor for the common mode signals, as well as an electrostatic shield.
The old issue of "ground loops" is a bugaboo that should be forgotten. It's really from the Audio world, and not the EM world.
If you do NOT connect both ends, you MAY be making a really good antenna to transmit (or receive) signals.
I once made a very effective radio reciever for tracking down some signals, which had an antenna that was a loop of wire. The wire was inside a copper tube. The difference was that the copper tube had a narrow slit in it. That made it from a shielded wire to an antenna.