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This makes me think about Vinylon[1] and this article from Reuters[2]

Vinalon is an organic polymer, like many other synthetic fibers we wear, but derived from coal instead of oil because North Korea has no oil.

The basalt fiber OP describes is not organic at all. It sounds more like asbestos actually.

Yeah, but the vibes are the same as basalt textiles

The Reuters article title is "Fabric made of Stone" (as it is made of coal and limestone), that is why it came to mind.