But see, that's the rub, isn't it?

If you owe debt to the failing bank, like a mortgage, the failed bank can sell your debt on to a different bank.  But the money raised through that process will go to shareholders and bondholders first.  After the dust settles, there isn't enough money left to cover what is owed to savers due to how fractional reserve works.

If the bank owe you money because you are an unsecured creditor, that debt does not get sold on to another bank.  It's a one-way street.  If you owe the bank, your debt stands.  If the bank owe you, that debt can and will be voided.  Again, you are only covered up to the amount your government are willing to protect.  Anything above that amount is likely forfeit. 

You, like most of the general public, do not seem to grasp this reality.  This has happened before.  It will happen again.  But not in Bitcoin.  Because we are not a debt-based system.