So you are lucky enough to accumulate a large sum of money way higher then the FDIC insured limits. I have no doubt you worked hard for this money and would be devastated if a failed bank wiped out your deposit. A golden parachute CEO over leveraged the bank and you are stuck with the bill the innocent depositor. It works like this when the FDIC takes your failing bank if they do not have enough to pay off the depositors your money is gone.
Let's say you had $1,0000.00 in the Banks savings account you would only be able to recoup $250,000 of that money. Most times the failing bank will be bought out by another larger bank and they assume all deposits but if there is no interested Bank the FDIC takes over and tries to get everyone there money back TRIES is the main word in this sentence. The best thing you can do to avoid this is to spread your money out over multiple Banks not associated with each other.
A little known tactic savvy people do is invest the whole Million or whatever amount it is into one bank that handles CDARS they in turn spread your money at over tons of Banks and you receive one statement in the mail from all the banks on your money. The rates are not as attractive if you shop for your CDs yourself but this is a fair tradeoff for ease of use and security. For the lazy at heart CDARS can't be beaten. This is how the rich insure massive amounts of money with no risk at all unless the dollar itself fails in this case all bets would be off anyway.