They can, but if it's a moulded plug then you need to weigh up whether it's worth the effort. If you know someone who can use a pair of pliers, wire-cutters and solder *electronic* stuff (not plumber's soldering or lead-lighting, but delicate stuff) they may be prepared to give it a go for you. See if you can find a nick in the cable to help them narrow down the fault.
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