I thought we were talking within the context of "serious problems". As for greece, well..it happened to Washington Mutual in 2008 - the largest savings in loan institution in the US. Of course, this is only one of many US banks which were not able to produce money when it was wanted in 2008.
There's a reason banks have a legal right to refuse a withdrawal, specifically because they may not have enough funds. That reason is: because it has and will happen.