[morzh]

Well....here it is.

The green stuff. Unfortunately, probably penetrates deep.
I opened the top layer and saw that:

The first wire was OK
   

But then the second wire showd this: Yikes!
   

So I started peeling the layers.
   
   

And as I  kept unwrapping, the wires were broken around the green:

   

So.
I doubt I should try unwinding the coil to see where the green stops. I am sure it will be a few millimeters deep at least.

I measured the coilm so I could do two things:

1. Order the new coil, new spider and reuse the cone.
2. Same thing, only with a new modern cone.
3. Screw it, use a PM speaker and a big a** resistor or a bigger a** choke.