> the tips kind of glow a bit, then just turn black. Which crumbles away, and i still
> have a frayed end
All is explained. Yeah, I suspected thiis would be the case.
What you have is not what you expected. The sheath is fine (some sort of meltable plastic), but the core is a different material. It could be cotton (unlikely) or it could more likely be rayon (cellulose acetate). These latter do not melt: they char.
Why is the cord made like this? There are two reasons. The first is cost: a rayon core is much cheaper than a Dacron or Spectra one. It may not be the main reason however. The second reason is what we call 'handle'. The softer core makes the string handle differently: usually softer and easier to work with. I will add that some steel cables also have a cotton or hemp core for the same reason: improved handle.
Well, that's all very well, but what should you do? You have several options.
1) Melt the end with a hot knife or soldering iron or similar (but NOT a flame) and press the molten sheath plastic into the rayon core - which may not melt. This keeps the core and sheath together, which is desirable. Gloves or tools are usful here and avoid burt fingers!
2) Work a tiny bit of epoxy or other glue into the end so it looks like the end of a shoe lace - again getting it into the core to anchor it to the sheath.
3) Peel the sheath back a bit, cut off 5 mm of the core, pull the sheath back out and melt it. This is quick and dirty, and can result in the core bunching up inside the sheath in a lumpy manner later on. I don't like it.
A report on your results would be useful to others.