To know whether the device you are testing is shorted, you need to be sure no other device is in parallel.
You need to be sure current is not able to go back through the wiring to another component.
To know whether a device is open, you need to be sure its terminals are connected to power (either from a supply or from your ohmmeter).
If there is an intervening component, and it is open, then you are not testing the device you think you are testing.
Sometimes you have no choice but to disassemble the headphones, and test each cable and transducer individually.
Be careful when hooking up an ohmmeter to earphones. It sends 1.5 or 9V out through its leads. This is likely to produce loud crackling noises, at a volume which depends on the amount of current available from the meter. The diaphragm may move violently, which can break connecting wires, or hasten the process.