It's common sense really - No low level signal should be screened by a cable where the screen can carry any current, because that current will induce noise onto those signal cables. If the piece of equipment at the remote end needs an earth, then you provide that earth via a separate means.
I must admit I once ignored that rule, installing prototype vibration monitors at a power station, on the big generators. They used a sort of tuning fork arrangement, inside a coil, inside a heavy duty cast box. I connected the sensor to the measuring instrument with two core screened, with the screen connected to earth at both ends. The small voltage difference between the generator and the instrument panel next to it, was enough to induce unwanted noises voltage onto the two cores and swamp the instrument. Cut the screen back - basically I nicked the screen through twice, half an inch apart, close to the sensor head, removed the screen and covered it with self amalgamate tape. Sensor head casting was earthed by being bolted to the massive generator casing.
Once that was done they worked fine and proved to be very sensitive and reliable. Idea was, if any undue vibration was detected, it triggered a warning alarm at the power station control desk.