As others have said (or implied), current is a loop, so you have signal (or send) and return paths, and without that you have no signal. If you stick a battery in a flashlight but only connect one end, you get no light. Cover the (-) end with tape, no current flow, no light -- this is the analogy to not connecting the ground at one end of an RCA cable. Chances are it will work anyway, but now the return is some tortuous path through whatever "ground" it can find, instead of tightly coupled to the signal in the cable. Probably very susceptible to noise and all that jazz.
I have used specialized coaxial cable that comprised inner and outer shield isolated by dielectric (insulation), but AFAIK all RG6 varieties of quad-shielded cable are a center conductor (copper or CCA), dielectric insulation, then shield layers that are not isolated from each other ("shorted together"). The shields are usually foil innermost, then braid, then another foil layer, then a final outer braided shield. The foil provides 100% (or nearly) shielding but is thin and easily torn, so the added layers of braided shielding and extra foil keep a good return path for cables that are run up antenna towers, outside runs, through walls, and other places where they may be damaged or flexed frequently and you want to ensure the shield integrity remains intact.
If you had an interconnect with an outer isolated (insulated) shield, the arrow could indicate the end at which the shield is connected (that is how it is used for XLR cables). Barring that, and my experience and limited searching says this is true, then there is no point in directional arrows on a single-ended interconnect. There is an exception I have seen: MIT cables and probably others may include an internal termination or filter network in their cables, and the arrows let you know which end has the filter. Let the debate about the advisability of using your cables as tone controls commence...
Note the signal path always needs two wires (someplace). A third conductor can be used for a shield in some situations.
For RCA cables, the signal return path and shield are the same. The "battery" is your source, like a DAC or preamp, and the "light" is your load, like your power amp. Both connections, shield/return/ground and center signal need to be made.
For XLR (balanced) cables, the signal send and return are usually a twisted pair (see post above with pictures), and those two are all that is needed to drive the load ("light it up"). The shield is a separate conductor, isolated form the signal pair, and need be connected at only one end to provide shielding for the signal pair.
HTH - Don
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) mats and belts on the LP12 turntable still in 'fruitbox' mode. You name it, we checked it for direction and thought/imagined we heard a difference (these are the days of the green pen on CD's remember). In the turntable's case, I soldiered on with this for a good while until I subsequently heard a deck two thirds the price (UK prices here) which needed next to no setting up other than tonearm and cartridge essentials and which 'sounded' so much more like master tape (I had copies and a well aligned Revox to play 'em on back then) irrespective of the direction of the sodding belt, which way up the mat should be or fuse in the mains plug 
