That is called the tinsel lead. It can be repaired correctly, or incorrectly. Its tempting to simply re-solder the wire back together. but, the wire will never be as long as it was originally when doing this, and it will leave a hard, non-flexible point in your tinsel lead where it broke (probably in the center). The right way to fix a broken tinsel is to completely cut off the old one, and re-solder on a new one, soldering at the two ends. This will leave the center of the tinsel lead flexible, where it needs the most flex.