During the Great Depression, small banks were subjected to “runs”-rumors would spread about a local bank. Depositors of the bank would get scared that the bank would close-leaving them minus their savings. Eventually, panic would break out, and everybody would head for the bank, hoping to get their money out, before the bank went bust.
There are pictures from the era, showing lines of people at banks, withdrawing their savings…picture the movie “Its a Wonderful Life” (George Bailey telling the depositors “your money isn’t here”!
Now, modern banks have access to government reserve banks-and so cash could be routed quickly to a bank experiencing a “run”. But suppose a bank in Athens opens up one morning, to find 5000 people outside-each determined to get their money out-could this happen again?
You can certainly still get runs on banks, just google for Northern Rock and you’ll find plenty of photos like this one from 5 years ago.
The UK government had to bail them out and ended up owning them.
There is very little danger that the banks will run out of money, the danger is that the money will be changed into a different currency. This could and probably will happen. To some extent it is happening already. What will probably happen if Greece decides to leave the Euro then they will close the banks for a short time while they replace the Euros with Drachmas and then try to set an exchange rate that does not cause a run on their banks. Everyone will want their money in Euros instead of drachmas so, whether this is possible remains to be seen.
This danger is not just in Europe, in Argentina they have place money sniffing dogs at the border to catch people trying to smuggle their money out.
If Greece leaves the Euro then everyone in Spain, Portugal, and Italy will try to get their money out of those countries. Whether there is enough money to back up the banks in this situation remains to be seen.