A rumor that Facebook would shut down by March 15 is a hoax, and there are a few reasons why it should not be taken seriously.
First the source. The Weekly World News ran the story on Jan. 8. The paper is known for publishing fictional stories about UFOs and the Bat Boy. A living Elvis is a common trope as well.
Assuming that isn't enough, it's worth thinking about the size of the investment from Goldman Sachs, made in the last two weeks. Goldman offered its clients a chance to invest in the company and the total stake amounted to $500 million. If Facebook were to shut down, that $500 million would have to be either returned to investors or simply lost.
Then there is Zuckerberg himself. While it is true he has more money -- at least on paper -- than most people could spend in a lifetime, the fact is he would stand to lose quite a lot of Facebook were to shut down. Facebook currently pays a large number of other businesses for server space, office space, and a host of services that every large company needs to function. It is a source of revenue for many companies that offer social games on the site as well as a source of data for advertisers. They would want to be compensated if the site were to shut down.
Another factor is how much of Facebook Zuckerberg actually owns. The Goldman stake, which values the company at about $50 billion, would be about 10 percent. The Russian company Digital Sky Technologies has reportedly put in a similar amount, taking up another 10 percent. If those were the only two investors that would be 20 percent of the voting shares that Zuckerberg would have little control over. Even if he owned a majority of the company it would be difficult if not impossible for him to simply shut the site down and walk away.