When I have synthetic cord that shows signs of unraveling, I snip off a bit to make a new end and then melt just the tip of it in a candle flame.
Kevlar doesn’t melt - it just chars if you get it hot enough to alter it. :-(
Also, since I am trying to get an approx. 0.020” thread (before fraying) through a roughly 0.040” round eyelet, the little “ball” of melted material that forms on the end of, say, a nylon string, using the candle flame method, would be problematic.
I briefly considered using braided fishing line, as it has almost as much strength as Kevlar thread / string for a given diameter, and I already have some in a 50 lb. break strength rating, but the Kevlar is much more abrasion and cut resistant, in addition to its higher temperature performance. Those characteristics may come in handy for some automotive uses, later on, too. :-)
This Kevlar “heavy thread” can actually be used to cut through soft wood, though that’s not the app I need it for at present.