1. When someone takes a crap and it sinks to the bottom of the toilet and is unable to be seen, therefore not needing to be flushed. Also means you must be sick enough to not wipe your ass after taking a crap.
2. The act of taking a huge shit and not flushing it, leaving it to flood for the poor bastard who uses the toilet next.
Joe is lazy. Whenever he has a nonflusher he gets up and walks away without wiping his ass.
John is an asshole. He just did a Nonflusher.