Xbox360 head-set repair
The cable had been pulled out of the head-set.
Taking it apart, I found that apart from the soldered wires, there was no cable-grip to hold it in.
I tied a figure-of-eight knot in the cable to give the case something to grip on, soldered the connections back and screwed the case back together - this was fiddly with the knot in the way, but worth it to have the cable held securely.
The connections were like this: