I went looking for this, because I had been saying that about 40% of the population of Greece was above 60, which is A Problem. Turns out that may or may not actually be true (altho it is certainly more true to say that 40% is over 60 than that 30% is over 60).
Anyway. This profile include death and birth rate, as well as migration rate (net number of people leaving the country. So: in per thousands:
just under 9 being born
just under 11 dying
just under 2.5 leaving
Since it isn't the over 60s leaving, you can imagine that the trend here isn't good.
Europe might contemplate treating Greece as a retirement community and not an actual member country, and producing a budget with funding sources from throughout the Union based on that way of thinking about it. Because that's what it is, and the only obvious source of potential immigrants that could fix the age structure is exactly the source of potential immigrants that Europe is desperately trying to prevent entering the Union.