Client Number Ten refers specifically to the unknown dope who rented Ashley Dupre right after Eliot Spitzer governated her in the name of the Great State of New York. In more common parlance, the term has come to refer to anyone getting another's sloppy seconds.
-Dude, I heard Henry's been hooking up with Valerie. I thought Tom was banging her.
--Dude, Henry cleans everyone's plate. Even his family calls him Client Number Ten.
-Shameless, that man.