Treasury Secretary Janet Yellen says the U.S. government won't bail out Silicon Valley Bank as it did with other financial institutions during the 2008 financial crisis, but she noted that regulators are working to ensure people and businesses with money in the failed bank would be made whole.

"The reforms that have been put in place means that we're not going to do that again," Yellen said when asked about a bailout during a Sunday appearance on CBS's Face the Nation.

"But we are concerned about depositors and are focused on trying to meet their needs," she added.

The fate of Silicon Valley Bank, or SVB, and its customers had been up in the air over the weekend, days after federal regulators took control of the institution following a "run" on the bank by depositors.

Customers had been flooding the bank with requests to withdraw their money, and earlier last week SVB said it had to sell bonds at a steep loss in order to meet those requests. That announcement worsened the panic over SVB's financial situation and led to even more withdrawal attempts until regulators stepped in.

The collapse of SVB marks one of the largest failures of an American bank since the 2008 global financial crisis.

SVB had carved out a niche in the banking sector by lending to tech startups, but the recent financial problems facing the tech industry put a strain on the bank, and caused its stock price to tank.

Yellen said that, despite the collapse of SVB, she believes the overall American banking system "is really safe and well-capitalized" and "resilient."

The Federal Deposit Insurance Corporation said on Friday that all insured depositors would have full access to their insured funds no later than Monday morning. The agency also said it would pay uninsured depositors an "advance dividend" in the next week, and that depositors would be sent a "receivership certificate for the remaining amount of their uninsured funds."

An independent federal agency, the FDIC doesn't use taxpayer money to insure deposits, but rather is funded through premiums paid by member banks and savings associations.

Regulators in the United Kingdom were also working on a plan to ensure that customers of SVB's UK branch were paid.

The bank's collapse has left tech companies and other SVB customers in limbo, and it's even caused headaches for others not directly connected to the bank, such as Etsy sellers who were told they may see delays in receiving payments because the online marketplace uses SVB to make some payments.