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Sounds like your little friend is starting to pupate. In time, it will completely enshroud itself with this web.
Just leave it undisturbed and in a couple weeks you may have an interesting surprise.
Usually caterpillars called woolly bears are the large and pretty Isabella Tiger Moth as adults.
Very nice find, I would release the adult moth (butterfly) as soon as it can fly to make more wooly bears.
My aunt keeps caterpillars, truly fascinating critters.