Wow, really interesting article here. How are those headphone wires so cheap and thin? The answer, they use enamel-coated wire instead of standard insulation around the wiring. That also makes them more prone to breaking, of course. This article goes through what needs to be done to repair such wires should you dare solder them yourself to repair.
20200829/https://hackaday.com/2016/11/22/iron-tips-soldering-headphones-and-enamel-wire/