Thanks Jeff.

Yes, the entire black plastic jacket of the cord is crumbling.
It's a coily similar to the cord on an old dial telephone;
cross-section a little smaller. Strain reliefs remain good.

On Monday, August 6, 2018 at 9:44:42 AM UTC-7, Jeff Liebermann wrote:
... repair the cord? ... liquid electrical tape ...

Interesting idea. There is a can on the shelf here. Uncoiled
the cord will be about 3-4 m long. Applying several coats of
liquid, neatly, could take some hours.

Your description reminds me that I've built a cord using heat
shrink threaded over the end of a bundle of insulated wires.
Three or 4 lengths of heat shrink with overlaps of a few inches.
The clear heat-shrink remains reasonably pliable after shrinking.

Since it was officially a medical device, unsoldering the
(molded) connectors and replacing just the cord, was not an option.

I have opthalmoscopes donated for use in the 3rd world. About
a half dozen of them have crumbling cord jackets. No clinic
in an industrialized country would accept the heat-shrink
repair but a hospital lacking beds for all patients won't
complain about an opthalmoscope cord which doesn't coil.
And the clear heat shrink allows inspection for a broken wire.
The cord hangs against the wall in a U shaped loop with power
box at one end and scope at the other. If the heat shrinks are
applied from the middle out toward each end, any liquid contamination
will shed off. Aside from that, overlaps are tight and I don't
visualize anything getting in.

Any further thoughts?

Thanks, ... Peter E.