Good to know we might have relieved a bit of stress, hope you get your issue resolved soon, please do not hesitate to get back to us if your fix does not work out as you might hope..
I suspect braided cables were designed to be used in situations where a high degree of flexibility is required, and in most cases I have seen they tend to be uninsulated. However I guess in vehicular use the lack of insulation/protection may expose them to corrosion. i.e. in parts of the world where salt might be used on the roads in Winter..?
Where a similar degree of flexibility may not be required an insulated flexible cable with heat shrink over the junction of cable to its termination will be better protected from such corrosion.
In the case of the need for a a highly flexible cable used as a earth return, there is generally no reason to insulate it, as contact with people or surrounding metalwork provides little to no potential issue of electric shock or short circuit..
As per gmg`s kindly supplied image... Many occasions of electrical circuit failure, tend to be caused at the point of a junction, such as at the the terminal that is crimped or soldered on to the end of the cable, or where that terminal connects to the component to be supplied with electricity.
Looking again at gmg`s braided cable pic, it seems perhaps possible that the point of connection braid to terminal, has suffered some reduction in current carrying capacity as a result of fraying of the conductors at the terminal, perhaps due to age..?
Any reduction in the Cross Sectional Area, of a conductor ( section cut through the copper wire) can lead to overheating at or near the point of partial failure, (reduction in c.s.a.) and in time along the length of the conductor, which generally shows up initially as discolouration at the point of failure, which can be masked up to a point by insulation until things really begin to heat up.
Once again using the image of the failed braided termination point, it seems a tad unusual for discolouration not to show all the way around the termination prior to total failure, perhaps a fastidious owner who likes to keep his engine bay clean and tidy, if not sparkling, might even have cleaned the accessible area of the braided cable termination which may have masked the issue as it progressed with time...?
In my case of using braided cable as belt and braces earthing, my Mog`s chassis was stripped and coated with two pack lacquer at the time of it`s "restoration" and the idea of drilling into it to provide better earthing points seemed less than desirable. Making use of a braided cable as an auxiliary earth, was a combination of thoughts at the time, in that I had that cable to hand, and possible future connections to it anywhere along it`s length, would be somewhat simpler than if an an insulated cable had been used.
As ever, just thinking in type, and more than happy to be corrected when I get things wrong....