I suppose almost everyone knows of the "trick" to use a little saliva (or a drop of water) to hold together loose ends of a cotton string or thread. However, I bought some 70 lb. braided Kevlar heavy thread (or call it darn small string), and despite being braided, the ends still fray somewhat easily, making it hard to pass through, say, a small eyelet. Saliva or water doesn't help much -- the Kevlar is a synthetic fiber that doesn't react "favorably" in this instance with water.
I wonder if soft clay rolled into the string would help?
Beyond that, I asked Brave Search for ideas on what would work best, and here is what it came up with:
https://search.brave.com/ask?q=What+adhesives+effectively+seal+Kevlar+fraying%3F&conversation=090a6c3d3a66a2a666589da83e2974a89651
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If I understand your issue properly i.e. getting a frayed, split end through something narrow, I deal with this all the time, trying to thread a fuzzy yarn end through the eye of a small needle. This is what I do:

I use an index card for my paper 'guide' - stiffer than regular paper, but not too thick.
Hot Glue Gun. Fixes pretty much everything!
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.