You are referring to a "floating shield" (one end 'floats' -- is not connected.) This is exactly to PREVENT any curent flow, which would result in hum and RFI being mixed with the audio signal (and thus winding up in your speakers!)
Having the shield connected at one end only does not prevent intercepted hum and RFI from draining to ground at the connected end.
In the old days ;~) single ended interconnects contained only one (center) conductor (+) and the shield carried the (-) signal, so it had to be connected at both ends. Then Bruce Brisson (owner of MIT cables) invented the "shotgun" single-ended interconnect while working for MonsterCable, which is what put MonsterCable on the map! It is called "shotgun" because it contains TWO signal conductors (double-barreled shotgun ;~) surrounded by a shield -- but since the shield no longer has to carry the audio signal, it can be 'grounded' at just one end, and can do its shielding job even more effectively.
Mr. Brisson provided these shotgun cables with ARROWS, which point to the end of the cable where the shield is connected to ground (no, the arrows have NOTHING TO DO WITH SIGNAL FLOW!) He did this specifically so that all interconnects could be installed with the grounded end of their shields connected to the preamp (yes, EVEN THE ONES BETWEEN THE PREAMP AND THE AMP!) That is because such a configuration is what's called 'Star Grounding' -- with the preamp at the center of the 'star'.
Star Grounding provides the quietest system; and in order to prevent ground loops, the preamp should be the ONLY component actually grounded to the wall. In the old days ;~) we generally put 'cheater plugs' on the (three prong) power cords of all other equipment, to prevent additional grounding points (which will always produce ground loops.)
Unfortunately, installing 'cheater plugs' can produce a, shock hazard if you are working on your system and remove the interconnects (and thus the ground connection) from a piece of equipment that has a cheater plug on it (for example: if you were adjusting the bias on a tube amp, which requires removing the input interconnects ;~) So be careful! Much of today's equipment (especially amplifiers) have switches on the back that allow you to 'float' (disconnect) that piece of equipment's audio circuits from ground, and thus eleminating the need for cheater plugs (the equipment's chassis is still grounded) and preventing you from accidentally electrocuting yourself!