When I sometimes have played in bands for civil war & other reenactors, there is often a dance which calls for one more gentleman than the number of ladies, and when the Music stops (it's usually a waltz), the gentlemen find a new partner. The odd man out has to dance with the broom. I take it that you are not referring to this quite fun dance?
As I recall, Fred Astaire & Gene Kelly (& other dancers) danced with a hatstand, a mop, & a mic stand, a broom, & probably a few other things I can't recall in various films--but not all at the same time of course.