I am quite familiar with the kind you mean. Some have bakelite diaphragms and some metallic (probably aluminum) unfortunately both are held by presses rings or collars.  I am not remembering rhe correct terms but you will I think understand what I mean.  These can be pried off to open the cases but I don't know of a sure fire method of restoring them.  It occurs to me that the rings could be cut in half, to remove them without bending or distorting them and replaced using superglue or other cement.

   If the phone measures open its mostlikely the transformer.  The elements ate 8 ohm Miniature speakers transformed to 300 ohms for the military version. Permo-flux made commercial versions in both low and medium impedance including stereo versions.  The internal transformers are very small. If the voice coil is open I think ots a list cause.

   It has also become difficult to find replacement headbands, ear pads, cards, etc.  These are very high quality phones designed at the Harvard acoustics lab to obtain high articulation in aircraft communication systems.  ANBH stands for Army-Navy-British-Headphone.  I am describing the ANBH-1. The earlier ANBH uses a different and smaller element.  I have not been able to find a way of disassembling them without destroying them.