They break. Wire is metal, and while metal can be bent in all kinds of directions, it does stress the material until finally, it breaks. Even a stranded wire, that’s made up of a bunch of very small gauge wires twisted or braided together, can and will develop a break or gaps at a point where all of the smaller wires have broken and pulled away from the connection point due to the movement of the casing material. It happens with all wires and cables, but headphones and phone chargers see the most frequent movement, and have thin gauge cables to begin with, so the breaks appear to happen more frequently with them.
It’s not always the wires that break, usually it’s the connectors.
Wires and connector pins are made of soft metals, mostly copper and gold, because they have low electrical resistance. Steel would be cheaper and stronger, but it has much more resistance and is subject to higher rates of corrosion.
These metals are expensive, so coatings are kept thin. On top of that, particularly in cell phones, space is very tight which also drives toward thin connectors and thin wires. This metal parts are subject to breakage, particularly when you don’t carefully remove any dirt/debris that might be on the connector before plugging in.
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