There's more than the FDIC. The government has shown over and over that it will bailout and/or nationalize financial institutions that could bring the entire system down (such as AIG). I'm not saying this system is perfect, but it's a LOT more robust and time tested than any cryptocurrency we have today.
It's the FDIC. The FDIC was created in the wake of the Great Depression to make sure bank runs stopped. And in the last ~100 years since it was created they've succeeded. [1]
Banks pay into the fund, which is used to make depositors whole in the event of insolvency. If the fund is exhausted, the FDIC also has a line of credit with the Fed. They have $125B of assets give or take, and a $100B line of credit.
That said, we haven't drawn on the fund yet, AFAIK. Even in 2008, when WaMu collapsed, the OTS took ownership of WaMu Bank and sold it to JPMorgan. [2]
[1] https://en.wikipedia.org/wiki/Federal_Deposit_Insurance_Corp...
[2] https://en.wikipedia.org/wiki/Washington_Mutual