Risk-free interest? In a bank? Are you kidding?
If you pick a large bank, your deposit is within the limit for federal insurance, I guess you could say it is risk-free.
Who insures the insurer?
The insurer is the FDIC and the FDIC is backed by the US government who can essentially print near unlimited amounts of money without causing massive inflation. The FDIC also can raise premiums that they charge banks for insuring the deposits.
So, if the FDIC runs out of money (because of multiple bank-runs), the U.S. government will print as much money as necessary to cover the FDIC deficit, thus making the taxpayers pay all the debts.
The FDIC should prevent bank-runs. The reason the FDIC would run out of money would be because insurance premiums would not cover losses.