No. Due to the previous crisis, is one part very well regulated. Here is what should happen...The emphasis below on unlikely is mine...
"A: In the unlikely event of a bank failure, the FDIC responds in two capacities."
"First, as the insurer of the bank's deposits, the FDIC pays insurance to depositors up to the insurance limit. Historically, the FDIC pays insurance within a few days after a bank closing, usually the next business day, by either 1) providing each depositor with a new account at another insured bank in an amount equal to the insured balance of their account at the failed bank, or 2) issuing a check to each depositor for the insured balance of their account at the failed bank....
...In some cases—for example, deposits that exceed $250,000 and are linked to trust documents or deposits established by a third-party broker—the FDIC may need additional time to determine the amount of deposit insurance coverage and may request supplemental information from the depositor in order to complete the insurance determination..."
"Second, as the receiver of the failed bank, the FDIC assumes the task of selling/collecting the assets of the failed bank and settling its debts, including claims for deposits in excess of the insured limit. If a depositor has uninsured funds (i.e., funds above the insured limit), they may recover some portion of their uninsured funds from the proceeds from the sale of failed bank assets. However, it can take several years to sell off the assets of a failed bank. As assets are sold, depositors who had uninsured funds usually receive periodic payments (on a pro-rata "cents on the dollar" basis) on their remaining claim."
"Deposit Insurance FAQs" - https://www.fdic.gov/resources/deposit-insurance/faq/