Facecrooks security notes a newer version of this hoax was found to be circulating 


QUOTE: The same rumors and hoaxes tend to circulate on Facebook time and again. There’s the classic viral message claiming that Facebook is going to begin charging users to access the site, and another popular rumor asserting that if you merely re-post a viral message, you can prevent Facebook from accessing your data. Another old rumor that apparently still has some legs asserts that Facebook will shut down imminently. 

Of course, this hoax is patently absurd; Facebook is a publicly traded company whose stocks goes for almost 27 dollars a share. It’s one of the biggest tech companies in the world; to announce that it’s going to be shut down because the CEO is stressed out is completely ridiculous, but, for whatever reason, people believe it. It’s important to treat everything you read with a healthy dose of skepticism, particularly on the Internet. Facebook isn’t going away anytime soon, and apparently neither are the hoaxes that spread on it.