zombie bank
n. A bank that cannot lend money because its liabilities are greater than its assets, but remains in business thanks to government support.
There have already been many measures designed to improve bank liquidity and none has had the desired effect. The Bank of England hopes that giving money directly to companies by buying bonds will ease this deeply worrying state of affairs. In the mordant wit of the City, we have created zombie banks: they have been brought back from the dead but they are not functioning properly. It is essential they start to work again.
—“The economy is on a wing and a prayer,” The Daily Telegraph, March 06, 2009
There's a reasonable chance — not a certainty — that Citi and BofA, together, will lose hundreds of billions over the next few years. And their capital, the excess of their assets over their liabilities, isn't remotely large enough to cover those potential losses.

Arguably, the only reason they haven't already failed is that the government is acting as a backstop, implicitly guaranteeing their obligations. But they're zombie banks, unable to supply the credit the economy needs.
—Paul Krugman, “Banking on the Brink,” The New York Times, February 23, 2009
1988 (earliest)
First Republic Bank is not alone. It is merely the largest and most immediate example. It is one of the "new breed of zombie banks" that is being kept alive only by regular infusion of taxpayer dollars.
—“Role of Financial Institutions: Hearings Before the Subcommittee on Telecommunications and Finance of the Committee on Energy and Commerce,” United States Government Printing Office, April 13, 1988
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