There's an old saying that goes, when you are in a hole, stop digging.

There's another one about all your chickens coming home to roost.

Both could be said to apply to the embattled European Union right now. No sooner had the bureaucrats managed to stave off the possible collapse of the euro caused by the Greek financial crisis by, as one leading commentator put it, kicking the can down the road a little further, than another crisis has arrived, once again with Greece at the center of things.

This time, it is the Schengen open border system which is at risk, and Greece's role in it.

The 26-member Schengen Agreement allows passport-free travel within the areas involved. In other words, once you have crossed into the area in, for example, France, you can then go seamlessly to Italy, Germany, Belgium, Spain and so forth, without having to show your passport or travel document.

If, for example, you are visiting from China, then you only need one visa to cover all 26 countries in the Schengen Area.

Two incidents have thrown the whole Schengen open-borders policy up in the air in recent weeks.

Last month, Islamic militants, some of whom had traveled back and forwards from Syria via the refugee trail into Greece, crossed from Belgium into France and slaughtered 130 innocent diners, drinkers and concertgoers before three of them died in a frenzied gun battle with police a few days later in a Paris suburb. One is still on the run, having apparently slipped back through European borders to Syria.

The response was immediate. France announced it was reintroducing strict border controls for the foreseeable future, as did Belgium.

Schengen, it seemed, was reeling.

But another body blow came when Greece, the preferred entry point for upwards of 750,000 migrants who have for the most part fled fighting and bombing in Syrian and Iraq, came under fire from some EU members, particularly in Eastern Europe, for failing to police its borders properly.

To be fair to Greece, the demands placed on it by its creditors have left it close to bankruptcy, and there's precious little cash left over to deal with the migrant crisis. Most of the arrivals want to head for Germany, after Chancellor Angela Merkel said her country would welcome them. The word magnet springs to mind, and that in itself is presenting huge social problems for Germany. But that's another story.

The issue of Greece's porous borders has caused some EU leaders to mutter darkly that Greece should be thrown out of the Schengen system.

That would be another blown to the eurozone, which is already facing the prospect of helping an ailing Portugal, and may well have to consider further economic aid to Greece.

In Brussels, the EU bureaucracy sails serenely on - it took an inordinate amount of time to respond to the refugee crisis, or the Schengen problem, and still hasn't done so satisfactorily.

In the meantime, the world continues to turn - China's Belt and Road Initiative, related to transport infrastructure projects, means enhanced trade ties between China and Europe, and whilst individual countries are actively pursuing closer ties with the country that is well on the way to becoming the world's biggest economy, I see very little coherent response from the EU.