Many headphones have two plastic-sheathed cables, one attached to the bottom of each speaker. The two cables meet in a plastic joint a few centimetres below the speakers, and then continue as a connected double cable until they terminate in a jack. (See picture below)
The problem with this design is that the connection between the double-cable sheaths is pretty fragile. It's not uncommon for the two cables to become separated after the joint. (Both cables are still sheathed; they're just no longer attached to each other.) You end up with a pair of very long single cables, which are prone to tangling.
Once a double cable has separated, or started to separate, is there any good way of reattaching it? I could tape them back together, but that would adversely affect the cable's flexibility. Is there some kind of glue I could use that won't make the cable too stiff? Or would it be possible to non-destructively heat up the cables so that the plastic sheaths fuse back together?