• The failures of Silicon Valley Bank and Signature Bank bring up old questions about just how safe your cash is at the bank.
• Here, experts answer what a bank run is, how FDIC coverage works and whether your deposits are still secure.

Despite the 2008 financial crisis, bank failures are considered extremely rare.

However, the unexpected shutdowns of Silicon Valley Bank and Signature Bank have many consumers concerned about their deposits, their bank and the U.S. banking system.

"Every American should feel confident their deposits will be there if and when they need them," President Joe Biden said Monday in an address aimed at easing fears as the U.S. Federal Reserve, the Federal Deposit Insurance Corp. and U.S. Department of the Treasury moved quickly to prevent a broader contagion.

Still, recent events bring up old questions about just how safe your cash is at the bank. Here, experts answer what a bank run is, how FDIC insurance works and whether your deposits are still secure.

What is a bank run?

Since banks take customers' deposits and invest those funds, that cash is not regularly on hand.

"When everyone wants to withdraw money at the same time, the bank doesn't have the reserve to do that and they go belly up, essentially," said Tomas Philipson, a professor of public policy studies at the University of Chicago and a former acting chair of the White House Council of Economic Advisers.

In a moment of panic, customers would literally run to the bank, Philipson explained. Now, that happens electronically. And because electronic transactions are made at high speed, bank runs are faster than ever — in the case of SVB, it was a dizzying 48 hours.

While SVB also had an unusually high percentage of uninsured deposits, there are other midsized banks that could be at risk of large withdrawals.

Could this happen at other banks?

The short answer is "possibly," according to Stacy Francis, a certified financial planner and president and CEO of Francis Financial in New York. She is also a member of the CNBC Financial Advisor Council.

"This is happening, in part, because of the Federal Reserve's sharp rise in interest rates," Francis said.

Banks own long-term bonds that are currently paying low interest rates, she said. When the interest that banks are getting on these longer-term bonds is lower than the interest rate that they are offering depositors on their savings accounts, less money is coming in than they are paying out.

Further, "many banks are seeing large withdrawals from cash depositors who are looking [for higher rates] to make more money," Francis added. "All of this is creating stress."

What about the cash at my bank?

Banks are covered by the FDIC, which insures your money for up to $250,000 per depositor, per account ownership category.

Since its creation in 1933, no depositor has lost FDIC-insured funds due to a bank failure. 

"Don't use worry minutes" if your cash is under the limit for FDIC coverage, said Carolyn McClanahan, a CFP and founder of Life Planning Partners in Jacksonville, Florida.

"You may have a short time without access, but the government has very speedy processes to get you back to using your cash in short order," said McClanahan, who is also a member of the CNBC Financial Advisor Council.

However, if you have more than $250,000 in deposits at any one bank, you may want to reach out to a private banker at your institution or split it into accounts at different banks, she advised.

"Another alternative is to move some to a brokerage account and use mutual funds that are invested in government-backed securities," she added. Some Treasury bills, or T-bills, are now paying 5% after a series of rate hikes from the Fed. 

How is this different from 2008?

"This doesn't seem like a financial crisis, yet," said Jude Boudreaux, a CFP and senior financial planner at The Planning Center in New Orleans. Boudreaux is also a member of CNBC's Advisor Council.

"The two banks we are talking about right now specialized in riskier assets," he noted, particularly, crypto and tech startups. "The likelihood that this becomes a national wave of bank issues seems low."

In 2008, irresponsible lending fueled a widespread housing bubble and when borrowers defaulted on their mortgages, the country's biggest banks were left with trillions of dollars in nearly worthless investments.

Those institutions are in a stronger position now because of new rules imposed after the financial crisis, including higher capital requirements and annual stress tests. 

Last year, all of the largest banks passed, but Moody's said that new concerns are surfacing. On Monday, the ratings agency cut its view on the entire banking system to negative from stable.

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