Yes banks have fidelity bonds called bankers blanket bonds (BBB) which cover losses from fraud, theft, etc. The FDIC doesn’t ensure against robbery, identity theft(banking fraud), etc. so this is an important protection for banks to provide.
They will cover the depositor's funds up to the 250k limit in the event of an event where the bank cannot return your funds, but banks assets or property is not covered under FDIC and need to be separately insured.