The banks with negative equities may suck taxpayers/fed cash to capitalize themselves. They may not let it pass to the economy, as they most likely engage in bringing their equities from negative values closer to zero using the cash coming from deposits and from the Fed printing press. Why does the government not use the new money (matched by funds from other investors) to build a fresh new bank for each bank that has problems. After it is done, the bank that has negative equity is then taken over, and the equity of shareholders and bond holders in that bank is wiped out. The government then creates new healthy banks, and clean the system from technically, but not legally, bankrupt banks. It would cost less than a fraction of what they have been spending doing so far, and the benefits will be greater.
Why? You keep same employees/buildings/etc. You just change equity holders. They did it in the airlines some years ago. A bank is not a difficult business as in other cases where it is hard to find customers, etc. The core of a bank is reserve capital.