My left earbud recently broke mid-wire: the bit that I like to fiddle with and bend. I fixed it, but I was wondering whether there are metals that don't work harden, or resistant to it?
The simple answer is No. Work hardening is result of plasticity. There are no perfectly elastic materials
Is there a way that you can treat normal metal to prevent it from, or at least reduce the effects of, work hardening.
Can these be used in headphones commercially?
As someone pointed out , Annealing is majorly used to soften a material so that its more workable. So essentially if you want to reverse the effects of work hardening this is the only route that is viable.
Work hardening leads to essentially hardening or strengthening till no further ductility is produced or material fractures or fails. If the material doesnt work harden or if there is no plasticity it is going to fail by brittle fracture at yield point.
The wires you mention can be produced/manufactured only if they show plasticity(or work hardening) in the first place, if they were perfectly elastic they couldn't be used due to risk of brittle fracture or low toughness.