This is very possible and it may get worse than that

FDIC may be eventually use up all its fund and go bankrupt as more and more banks go under. This is not the worst thing that can happen. Eventually, the US government could be overwhelmed by the debt from 2F and go belly up. If that happens, the US dollar will be cheaper than the money it is printed on. I hope that does not happen. But the possibility cannot be ruled out.