The act of someone approaching you to hit on you, then deciding not to. Similar in context to an uninvitate, in which the inviter takes back their invitation.
When someone is hit on at a bar by someone who is so drunk that their pick up lines are a little sloppy. The sloppiness also relates to the dribble from their inebriated lips.
I was at Joe's the other night and got sloppy hit on by DrunkSue.
To romantically chat someone up, then bail before significantmutual feelings develop.
Casanova and Don Juan were infamous as expert "hit on and run" dandies --- Don Juan had so many flings, in fact, that when presented with a number of his former lady-friends in the afterlife, he could not even remember the names of any of them.