It's an inductor, made using a multi-hole ferrite bead with three turns of tinned copper wire through it.
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Ferrite 44 Material. 1 1/2 Turn.
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Functionally, they are electrical "noise filters" to reduce the emitter radio noise caused by the motor commutator sparking, and not anything that can fail or cause a problem, other than the connections breaking.
You could bypass it with no effect on how the machine worked, though technically it could start to cause radio interference when in use.. They are fitted to allow it to comply with EMC (interference) regulation.
Or if you can find some singe strand copper wire the same thickness, you could replace the wire yourself to give longer ends & make it easier to refit; or unthread the short end to get more free wire and just leave two turns through it.