In the first season (Season 01 Episode 05: Meeseeks and Destroy), Rick gives the Smith family a Meeseeks box to get them off his backs. From the actual script:
Rick: As for you dingdongs This is a Meeseeks box.
Let me show you how it works.
You press this.
Meeseek: I'm Mr.Meeseeks! Look at me!
Rick: You make a request. Mr. Meeseeks, open Jerry's stupid mayonnaise jar.
Meeseek: Yes, siree!
Rick: The Meeseeks fulfills the request.And then it stops existing.
Later we find out that the Meeseeks cannot die until the requests are fulfilled. But when Jerry's requests go out of hand and a bunch of Meeseeks fail to fulfill his two-stroke request, they all decide to kill him.
Although, it all ends well for both the Smiths and the Meeseeks, had they been successful in killing Jerry, would it be suffice for the to no longer exist and go back to not-existing anymore?