By Peter Eavis Hillary Rodham Clinton said this week that, if it came to it, she would let a big bank fail — and it would not be surprising if other presidential candidates adopted her anti-bailout stance. But regulations introduced since the financial crisis of 2008 have, in theory, already made it much safer to let a bank die. And on Friday, the Federal Reserve proposed a new rule that aims to make the process of winding down a faltering financial giant smoother still. It would require banks to have a bigger financial buffer that could absorb potential losses on loans and trading positions. The new regulation seeks to inflict the costs of a failure on investors who have lent to an ailing bank and on its shareholders, rather than on taxpayers. The hope is that the rule would work without greatly disrupting the wider market and economy. “The proposal is another important step in addressing the ‘too big to fail’ problem,” said Janet L. Yellen, the Fed chairwoman, referring to the notion that the government has to bail out big banks because letting them fail would cause severe collateral damage in the economy. Of course, there can be no guarantee that the authorities would let a large financial firm topple in a future crisis, especially if several big banks are teetering at once. In 2008, soon after Lehman Bros. collapsed and the global financial system seized up, government officials dropped their opposition to bailouts. At the very least, though, the new rule and related regulations could force investors to think harder about the risks of backing financial giants. And if large banks have to consistently pay more for their financing, they may decide to shrink to make their businesses more profitable. “The proposal should also improve market discipline,” Daniel K. Tarullo, the Fed governor who has spearheaded several new banking rules, said in a statement. The banking industry, perhaps wanting to avoid harsher measures, has mostly embraced the system of winding down large banks that was set up under the Dodd-Frank Act, which Congress passed in 2010 to overhaul the United States’ shaky financial system. Still, the Fed’s new rule, which focuses on the country’s eight largest banks, like Citigroup and JPMorgan Chase, could increase costs for an industry that has already borne the burden of hundreds of new regulations. The Fed estimated that the eight banks would currently need $120 billion combined to meet the requirements of the new rule. The banks may not need to issue large sums of additional debt and equity to make up that shortfall. Even so, the Fed estimated that the banks’ combined cost of financing themselves could increase by as much as $1.5 billion a year. The banks and others, including the public, can now submit comments on the rule.