No, because when the FDIC takes over a failed institution, it calculates the interest you've earned right up to the day the bank went belly-up, and it posts all the interest to your account. It's done by arranging your investments in different types of individual, joint and trust accounts. Keeping in mind the Rule of 1's, here's how it's done. This is a little more complex. And it's legal.
Mutual funds are a different animal.
They do not have FDIC protection, even though their yields pay more than insured CDs.