Kelim, Chapter Twenty-Two, Mishnah Three
1) A bench, one of whose legs was removed, is clean.
a) If its second leg also was removed it is still clean.
b) If it was one handbreadth high it is unclean.
2) A footstool one of whose legs was removed is unclean.
3) The same applies to the stool in front of a cathedra.
Section one: A bench has two legs, one on either end. Clearly if one leg is removed, the bench cannot be used and it is pure. The same is true even if both legs are removed. One does not sit on a bench when it is simply a board on the ground, because it is usually too thin.
However, if the bench-board is at least one handbreadth high, it is unclean because a person might come to sit on it.
Section two: A footstool can be used to put one’s feet up even if one of the legs has been removed. In other words, a footstool does not have to be exactly upright because one doesn’t sit on it. Therefore, since it can fulfill its original function, it remains unclean (or susceptible to impurity).
Section three: A “cathedra” is a couch used by the upper class (same word as cathedral). The stool in front of it has the same rule as does a footstool.