Maybe a fake of a fake?

[McCreed]

As for a broken coil wire, I'd have thought that would put the resistance up rather than down.

Yes, a broken coil wire would give an open circuit.

I must be confused. Two times I have fixed a single coil pickup, that the coil wire was broken away from where it is soldered to the lead on the bottom bobbin. I don't recall them reading a higher DCR than they were supposed to. IIRC both read 0 ohms.
Am I imagining that, or is it different in a humbucker? Please explain.

Sincerely,
Electronically Challenged

[Simon Barden]

I must be confused. Two times I have fixed a single coil pickup, that the coil wire was broken away from where it is soldered to the lead on the bottom bobbin. I don't recall them reading a higher DCR than they were supposed to. IIRC both read 0 ohms.
Am I imagining that, or is it different in a humbucker? Please explain.

Sincerely,
Electronically Challenged

You must be confusing an open circuit/overload reading with a short/circuit 0 ohms reading. If the wire has broken away, how can you have a circuit? And if there's no circuit, you've got an infinite resistance reading. I don't know exactly where you were measuring across, but if you were measuring across the min lead connection solder joints on the pickup, you would have got an open circuit reading.

Now if someone had been passing sufficient voltage/current through the coil to burn the insulation off, then you could get a near 0 ohms reading and no output, but that is very far from a broken wire and very unlikely to ever happen short of extreme stupidity like trying to plug the guitar lead into the mains.