You can try to re-solder it but make sure you use a heat-sink and flux. The problem with small earphones is that it's a wire within a wire - for visual purposes picture it like the coax cable that goes in the back of your TV. If the inner wire is missing you can't just strip the wire to get it out because you need to keep the two from touching. If you don't mind spending a small amount of money take it to your local electronics repair store and they'll reconnect it for a small fee.

Happy Holidays and good luck!