The big danger inherent in a bank is a liquidity crisis-- their loans can't be called in all at once and their assets generally can't be sold all at once withou

The big danger inherent in a bank is a liquidity crisis-- their loans can't be called in all at once and their assets generally can't be sold all at once without losing a lot of value, but their liabilities in the form of demand deposits can be withdrawn at any time. So in the modern era central banks generally stand as a lender of last resort, if all the depositors want their money out at the same time then the central bank will lend individual banks cash against their assets to give to depositors. This promise, if made credibly, has the effect of preventing bank runs. The Greek banks have a different problem, a solvency crisis. They have made investments and loans that have not done well, in part because the economy as a whole has not done well. That includes lending money to the Greek government in the form of bond purchases. So it is simply the case that their liabilities (including money owned to depositors) are greater than their assets (including the risk discounted value of outstanding loans).