This phrase is derived from the the term blue balls. Being left sloppy is the same as being given blue balls. Although this phrase can be commonly used in situations where you were left hanging by someone.
(Someone doesn't shake your hand after you put your hand out.) "Damn bro you really gonna leave me sloppy like that?"
Guy 1: Did you fuck last night?
Guy 2: Nahhhh I got left sloppy
Sloppy left overs is basically your ex who gave sloppy head
Have fun with my sloppy left overs