But they passed in part by using a legal but dubious accounting method, in which they counted anticipated tax breaks as capital. That practice, allowed in several other eurozone countries as well, is being phased out by regulators and is considered especially risky in Greece, because a bankrupt government would probably not be able to pay refunds due to taxpayers.

“This accounting option has long been viewed with a great deal of skepticism in many quarters,” Andreas Dombret, who is responsible for bank supervision at the German central bank, the Bundesbank, said in an email. “It is a particularly dicey thing to do when the sovereign is struggling financially like in Greece.”

Problems at the Greek banks began mounting in the prelude to the election of the left-wing Syriza government in January and have continued ever since. Depositors fearful that Greece would drop out of the euro shipped €30 billion abroad or squirreled it away in their homes from the end of November to the end of April. The government contributed to the deposit outflow when it raided the bank accounts of state entities to meet its basic financial obligations.

The banks have been surviving on a drip feed of emergency cash from the European Central Bank. But the central bank would be forced under its rules to cut off the funding if Greece could not reach an accord with its creditors.

If there is no agreement between Athens and the creditors, the consequences would be dire and unpredictable. People who have not already sent their money abroad or hidden it under a mattress might storm the A.T.M.s. Desperate to stop the flight of wealth abroad, the government would impose restrictions on money transfers, so-called capital controls.

In the worst case, Greece would drop out of the euro; remaining loans and deposits would be forcibly converted into newly printed drachmas which, according to some estimates, would immediately lose about half their value against the euro.

If the government defaulted on its debt, Greek banks would suffer disproportionately because they own tens of billions of euros worth of Greek bonds. The country and the banks might then go down together in a fatal embrace of mutual dependency.