What's the bad news if my speaker doesn't work and shows 1 ohm?

Shorted coil. Recone or bin.

 

The ohms have left the building!

 

It would help if we knew the make and model of the cabinet and of the driver within it.

 

True, many Bose drivers are in fact 1 ohm voice coils... (not common, but possible)

 

Well if you are measuring directly from the loudspeaker terminals with an accurate meter with all cabinet wiring disconnected and thus not figuring in the equation, we can say for certain that you have a short circuit in your loudspeaker.
As I would imagine your loudspeaker was produced in both 8 and 16 ohm nominal impedance versions, if it was 8 Ohms impedance it would read less on the meter as the meter is reading DC Ohms resistance not impedance.
This is an 8Ohm nominal driver.

Shows 5.6 Ohms DCR on a military grade fluke meter.
"your mileage may vary"

 

Bad neighborhood?

 

Nope just mis spent my youth in marine engineering with that. It's handy that it floats and is waterproof.X

 

This is perfect if you own an amp that runs at 1ohm.

 

Another possibility is that you have lost your hearing, and your meter is out of calibration.

 

Here's 4 more. Now you have 5.


Seriously though, good luck with it.

 

Inspect the speaker’s tinsel connections, at the terminal and at the cone where the coil connects. If in doubt, resolder the terminal connections.

 

I've been told that my meter's out of calibration. But enough about me.

Onward to the search of a one-ohm or less safe bass head.

 

You might know, but... Be sure to unplug the speaker from the wiring before measuring.

Sadly, it's probably toast anyway.

 

This won't cause a 1 ohm reading.

 

True, but show me a typical hand held ohm meter that can accurately read 1 ohm. I'm not convinced that the reading is correct. It makes sense to closely inspect the speaker for issues.

 

Agreed, but a damaged tinsel wire typically reads high or open.

 

A shorted coil reading low ohms and no rubbing with free movement of the cone doesn't usually add up. Maybe enough ferrous particles in the coil gap.