It's another iteration of the idea that while capital should have no restriction to movement, movement of people should be strictly controlled.

Might be an idea for you to search the subject of Schengen Visas and the Schengen Agreement.

In other words; it's fine for the EU members to demand austerity measures from Greece, to command Greece to commit self-rape for their banks, and to levy other financial punishments and exploitations upon Greece. But it's not acceptable for Greek people to flee from their nation's ever-worsening economy into other members of the "union."

The money can move freely, but the people have to stay put.

"if one state persistently failed to stop illegal migrants from entering Europe's Schengen zone."

Greece and most of the European countries are members of the agreement.

So the rich people can move themselves and their money anywhere they want but after those same rich destroy a country with their money the citizens of that country better stay put.

It's just another way to make their money more valuable and to make citizens just another commodity.

If Greece does decide to pull out of the Euro they'll impose exchange controls to prevent flight. Switzerland has already mentioned such controls for inflows to prevent "hot money" inflating the Swiss Franc - they'll limit transfers into Swiss Francs.
IF the Euro did collapse completely , which I would doubt anyway , then almost anything goes. No individual country could withstand a sudden increase in load on its state provided services e.g our NHS here in the UK.

As I mentioned above the emphasis here seems to be more on the issue of countries which border the Schengen Group securing their own borders from illegal immigrants. France wasn't too impressed when Italy granted temporary visas in bulk early last year in the full knowledge that most they had issued those visas to would cross over to France almost immediately.