High temperature
heat shrink is not flexible. It's only servicable use in in covering high temperature
butt splices as needed when attaching the lamp
base to a cable
whip as opposed to using the leads of the lamp
base in a fiberglass sleeve in going to the
plug.
Problem it would seem both Mayhem and I have is that we don't really understand by your words which
conductor it is that is exposed, which of the above two systems is in use, or to what extent the damage is to which part in recommending a solution of replacement. In most all conditions, replacement will be necessary unless the
ground in which case it's possible you can possibly fiberglass electrical tape it due to it being a
ground and not mattering if it touches the frame as it does already.
On the other
hand, given you had enough slack that some of the conductors got caught in the cap, it might be possible to high temperature
butt splice the thing and either
cover the splice in either the high temperature tape or use the high temperature
heat shrink. This is possible dependant upon the general condition of the cable in question that I would want to look at.
Short of this, I recommend you either replace all infected components, or take it to a qualified service person to have a look at it. Just can't confirm such a thing anyway as what to do.