In a typical situation you can not allocate a particular XLR cable to just one mike, and cables move tasks freely in a studio or live rig.
Please confirm that the XLR cable in question was connecting to a microphone, not between two other components.And, I repeat: an open shield on even one side can lead to hash/noise in the mic.
It was indeed a cable going to a microphone! (So: connected to nothing else.)At the moment pin 1 of the XLR on the microphone input was connected to the shell of the connector (=mains ground), a clear mains hum was audible. (I suppose this was due to a design fault in the mixer. This happened on every channel.)
... chassis ground connected to audio ground is the norm in most vintage supplies.