Balancing the books can easily be achieved in a closed, nationalized, digital banking system, so long as liquidity can be kept from leaking out in the form of physical cash withdrawals or transfers to foreign banks. Money transferred digitally within the system can always be found somewhere and borrowed back by the bank from which it was transferred, balancing its books.
The remaining question is, how to deal with leakage in the form of cash withdrawals or transfers to foreign banks? One radical possibility would be to go all digital: cash would no longer be official legal tender after some designated date. President Roosevelt did something similar when he took the dollar off the gold standard and ordered people to cash in their gold for paper dollars in 1933.
That approach, however, is highly controversial. Ideally, it could be avoided by simply paying an attractive digital bonus for depositing physical cash in the banks, and paying an attractive interest rate to keep it there. A sizable fee could also be charged for cash withdrawals or transfers outside Greek banks. This would not actually be a "haircut," since the digital euros would be available for use at full value so long as they were transferred by bankcard or check within the digital banking system. The transfer penalty could be phased out over time as cash deposits were built up. In effect, the money would just be on loan at interest to the banks for several years.
Another alternative would be to run the euro printing press at the Bank of Greece, something that is apparently being done quietly already. As precedent, Ireland's central bank quietly printed 51 billion in 2011.
Another much-discussed alternative would be for Greece to leave the EU and simply issue drachmas. But as of this writing, it looks as if the creditors have strong-armed Greek leaders into accepting their harsh austerity measures in order to stay in the EU.
Greece blazed the trail globally for political democracy, but modeling a sustainable economic democracy may have to wait for another day.
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