I'm sorry to bring you bad news, but the most likely thing is that the copper conductor has become fractured inside the wire. The best you can do is to carefully identify which end of the wire has become broken (it usually happens at an end, where it goes in to an earbud, or a plug) and cut it back to the break, and then pry open the bud, cut back the insulation and re-solder the conductors. This is a pretty involved process, and to be honest, even with all the tools, I wouldn't attempt this. Oh, and plugs are usually moulded, so you can't do it, but if you try to buy a new plug in a store it will cost almost as much as new earbuds.