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Headphone wires do give out from repetitive strain, esp. when the cord is yanked on hard, put under that sort of strain, or is bent repeatedly at a point or points on the cord.
(So, bundling up the cord in a tightly bound loop, repeatedly, will shorten the lifetime of the cord to the headphones, for instance.)
It is likely that the wires inside the cord have become somewhat broken, but bits sometimes fit together at certain positions. Unless the cord is visibly either bulging abnormally at any point, or is visibly broken, then otherwise the insulation is less likely to give way than the delicate multi-stranded wires inside the headphone cord.
Basically the headphones are unfortunately both 'broken', in all likelihood - as far as the cord is concerned - and also, at 4 years old, long out of warranty.
Is there any other advice I can offer you? about this problem.