The Fed officially adopted a new rule Monday that limits its ability to lend emergency money to banks. 

In theory, the new rule should quash the notion that Wall Street banks are "too big to fail." Translation: the government has to save them during a crisis. 

The Fed's new restrictions come from the Dodd-Frank Act of 2010, which brought in a wave of reforms after the financial crisis. 

Under the new rule, banks that are going bankrupt -- or appear to be going bankrupt -- can no longer receive emergency funds from the Fed under any circumstances. 

If the rule had been in place during the financial crisis, it would have prevented the Fed from lending to insurance giant AIG (AIG) and Bear Stearns, Fed chair Janet Yellen points out.