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