What happens to the shares when the public company like Facebook shutdown?

[Ray]

Your questions are too simplistic. What do you mean by "when a company shuts down"?
A company may start to lose money and run out of cash to continue its operations (like pay their employees). The company then becomes insolvent (not enough money to pay creditors). It can then file for voluntary liquidation or one of its creditors will file for compulsory liquidation. Maybe receivers will be appointed to run the company down in an orderly fashion. Assets have to be sold to pay secured creditors and then unsecured creditors. The share price will collapse. The stock exchange listing may have to be cancelled.
The share quote may be used to reverse a new business into it (shell). etc. etc. Whatever happens it is bad news for the shareholders: they are unlikely to get any money back as they are last in the queue and usually get shafted.