How would the Federal Deposit Insurance Corporation help prevent another depression?

Answer 1

In and of itself, it wouldn't. The Federal Deposit Insurance Corporation is not an insurer per se. Instead, it is a quasi-government agency that uses tax dollars to prop-up and try to rehabilitate failing banks.

The FDIC "insures" deposits to a stated amount per depositor. Therefore, if the bank fails, the FDIC reimburses the depositor for the amount that he/she/it had deposited up to the stated amount.

While "bank runs" can be an elements of a "depression", there are many other causes of one. One of the primary causes is reduced demand for goods and services in an economy, which results in reduced employment, which in turn further reduces the demand for goods and services.