Nobody quite knows what it means for a bank to be "too big to fail," so the regulators in charge of solving the problem have an understandable focus on tidiness. A bank that fails tidily, sensibly, in neat little compartments, probably won't do much damage to anyone else. A bank whose failure is sprawling and incomprehensible might well turn out to be catastrophic.
So the preferred mechanism for winding up a possibly too-big-to-fail bank these days is largely about compartmentalization. You put all of the important, messy stuff into subsidiaries -- put the deposits in a bank subsidiary, the repurchase agreements and derivatives in a broker-dealer subsidiary, etc. -- and put those subsidiaries under a "clean" bank holding company with a fairly large amount of capital and long-term debt. Then if things go horribly wrong, the holding company's shareholders and bondholders are the ones who lose money, shielding the people who have messier and more systemic claims on the subsidiaries. The regulators swoop in and recapitalize the holding company, or just sell the subsidiaries to other, healthier banks, in any case without ever interrupting service at the systemic subsidiaries. All the bad stuff happens at the holding company, all the important stuff happens at the subsidiaries, and you try to avoid mixing the two. Then all you have to do is make sure that the holding company has enough equity and long-term debt to shield the subsidiaries against any plausible bad outcome.