Yes, that looks broken! Have you fixed it? You said that you've reassembled it.
If not, it's possible to solder another bit of wire between that and the ground wire connection, though it will be very fiddly to do. You'll first need to push the red and black wires all the way back up through the hole in the baseplate, then unsolder the black wire and suck all the solder out of the hole. Then solder a thin bit of wire to the broken coil wire (hardest bit when its so thin). Heat from the soldering iron and solder should burn off the wire's insulation.
Then put the other end through the hole, put the black wire back in the hole as well, then solder it back up. The baseplate will probably be connected to the black ground wire as well, either directly, or via a short wire link, so make sure that's all electrically connected.
Then push the red and black wires back down through the centre hole and you should be OK.