Never seen one but assuming you have a plastic coil & the wire has broken off flush with the surface.
You can follow the wire in with a soldering iron until you have enough to solder to, then epoxy the join & cable-tie the wire so if it gets pulled on it won’t break. Scary part is you don’t want to hit any other wires so aim away from the other wire, maybe toward the outside of the case.
There will be residue on the wire so a grunty flux will help you tin it.
Clean the soldering iron well as this residue ain’t the best for it.