Since the 1930s, "resolution" is what the FDIC (Federal Deposit Insurance Corporation) does when a bank it insures fails. FDIC bank supervisors determine that the bank’s assets are worth less than its liabilities. The bank itself is shut down and its assets are transferred to a new entity controlled by the FDIC. This is a form of bankruptcy process managed by a government agency - with the responsibility to manage an orderly liquidation and to avoid losses to insured retail depositors.
The FDIC attempts to maximize the value of the assets it acquires, typically by selling them to another bank or banks. From the customers’ standpoint, little changes during this period: the branches, ATM machines, web site and so on remain in operation during the transition, except that customer may not be able to withdraw amounts above the insurance limits.
If the proceeds do not cover the bank’s liabilities, the creditors lose out, but the FDIC makes sure that all the insured deposits are paid back. Note that going into conservatorship does not mean that the bank is consolidated onto the government balance sheet; the liabilities are not automatically guaranteed.
The FDIC previously implemented resolution only for banks with insured retail deposits, but under the Dodd-Frank Act of 2010, the FDIC is empowered to use the same process for bank holding companies and other financial institutions. It remains to be seen how this will be implemented for very large cross-border banks, particularly as there is no cross-border counterpart of the FDIC’s resolution approach.