carefully hack saw the crimped metal all around, try not to touch the underlaying insulation of the wire you want a anular cut near teh housing to reduce the length of the crimped section, this should expose some good insulation and wire. now you can be able to solder a new wire to teh old one after you trim it. then heat shrink sleave it all up. this is how I have done it and it works!! I suggest fine teflon insulated wire is used.
Yes it can be done, mine looked very much like yours before repair.
you can probably only do this repair once, so take your time
solder will NOT stick to that oily wire end, so use some good contact cleaner or laquier thinner or both to complete clean up the oil on it, then tin each wire end before soldering them together,
if you have any other vlave, besure to re-inforce teh original wire with some short lengths of shrink sleave at teh crimp a layer or two of sleave will act as a strain relief to prevent sharp bends, that is what does these wires in.
also use a high grade repair wire that has thin strand, thick strands will not be a flexable, more likely to re-break.
good luck, take your time, go slow, clean it well beofre solder you dont want ot monkey around with a dirt solder joint as it wont work, and you will over heat teh wire trying to get it to work.
you aosl could take the whole unit part and remove the crimp an dtry to re-wire that way, but give the first appouch a try first.
these are salvageble !!!!!!!!
PS the wire must NOT touch the metal can nor crimp. only insulated wire can touch!!! else you short it out!!!