A drug dealer or hookup that is either bunk or doesn't deliver. a Fall-Through is the kind of guy that makes you wait 2 hours for a bag of weed, only to tell you he couldn't get it. A Fall-Through is the ultimate timewaster and ultimately, an asshole.
"Tony can't get weed, he's a fall-through"
"Bob said he has shrooms? 10 bucks says he's a fucking fall-through"