From the Wall Street Journal:
The steady outflow of deposits from Greek banks hasn't yet turned into a full-blown bank run, and the European Central Bank has nearly limitless capacity to provide banks with additional liquidity. But economists have long warned that a run on banks could develop if the population fears Greece's departure from the euro is imminent and that their savings would evaporate. A bank run could trigger the euro exit if it reaches a scale that forces Greek authorities to freeze bank accounts and print their own currency to keep the financial system alive.
What is more, if Greece fails to comply with the conditions of its bailouts, the ECB would likely cut off the liquidity support for its banks, a move that could cause the banking system's collapse.
It is simply unbelievable that at this point in history, more than 100 years after Bagehot's Lomberd Street, that we could consider that the European Central Bank will not only fail in its role as lender of last resort for the fiscal authority, but also fail in its role as lender of last resort to the banking system. Yet here we are.