Higher quality, braided cables, if it’s an option.
You could also try shrink tubing around the damage prone areas. Specifically shrink tubing that has the glue lining, that bonds when heated.
The cable is attached to the headphoes so the first isnt an option, Will the shrink tubes prevent the cable from rotating?
Not if you just apply it to the broken area, up to the 90 deg angle of the cord.
I admit though, I’m not sure the best way to address the wires that are already so exposed. Because I’d imagine there’s currently risk of shorting.
Was reffering not if the plug will rotate in the jack, but if the wire will rotated relative to the plug, how it shouldnt br. The wires are insulated and still work tho