While the fleecy referred to a tuft of wool or sheepskin, which also gave its name to the overskirt worn by students in Halle in the 18th century, fleecy are individual tufts of wool flying around or loose thread ends.
Today, you simply suck them up with the electric vacuum cleaner, which was invented around 1900. But some still have all sorts of free thread ends and other fluff flying around. In this case one still occasionally speaks of fluff.
Source: Lexicon of Endangered Words | Bodo Mrozek