Best practice for layout of balanced audio grounds
Quite often, the screen is connected to chassis to (a) dump any interference noise to the chassis and (b) blow any fuses should the screen become live. Of course, assuming chassis is metal, and with a mains ground connection. Failing this, PSU 0V is probably the next best.

It's also not unusual in stage and/or semi-pro gear which may be connected to god knows what, for that connection to be made via a "ground lift" switch, to prevent ground loops where the screen is grounded at both ends to different sides of the studio/theatre/etc. Given a choice, the screen should be grounded at the receiving end of a line, so that it is close to the receiving end's ground potential. Leave the ground lift in the "connected" position where possible (see link above).

With regard to plugging into an unbalanced jack: that effectively shorts ring and sleeve together. The ring forms the audio signal return. If the sleeve introduces noise or  ground loop hum from chassis, the ground lift switch should take care of that.