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1.
When two people are sitting in adjacent restroom stalls waiting for the other person to drop the first turd. If no one deploys their first bomb after several minutes, a plop off is underway.
Hey Carl, where have you been the last 20 minutes?

The restroom. I got caught in a plop off with some guy wearing penny loafers.
by His Royal Phatness October 09, 2013
 
2.
A rule in water polo. The referee plops the ball into the water when a foul has been committed between players of the opposing teams, but it is unclear which player is guilty. A plop off is carried out to fairly restore normal play.
Oh man both players went at each other there - we need a PLOP OFF!
by remesas March 02, 2011