Fulling - for wool at any rate-- was done with a sort of clay-The clay absorbed some of the lanolin that was left in the wool-- so the dry clay was pounded into the cloth to clean it of natural oils.

You can also use dry clay to "clean" cloudy wine of sediment-- (but its not called fulling-- Its done with cheap wines that come from second pressing of the grapes, and has more "pulp".) With soup or broth-- you use broken egg shells to clear the sediments-- I don't know why it works-- but it does.