Securities are not covered by FDIC, but they may be covered by SIPC.
SIPC protects, in summary:
SIPC protects against the loss of cash and securities – such as stocks and bonds – held by a customer at a financially-troubled SIPC-member brokerage firm. The limit of SIPC protection is $500,000, which includes a $250,000 limit for cash. Most customers of failed brokerage firms are protected when assets are missing from customer accounts. There is no requirement that a customer reside in or be a citizen of the United States. A non-U.S. citizen with an account at a brokerage firm that is a member of SIPC is treated the same as a resident or citizen of the United States with an account at a SIPC member brokerage firm.
What it means is that if a brokerage fails, your investments are insured. So if due to the brokerage failure your 10000 shares of MSFT disappeared, the SIPC will get you a bit over 2000 of them back (up to $500k value). The rest may or may not be recovered as part of the investigation and liquidation.