It's not looking good for them. For years they covered up the problem and now it is punching them repeatedly in the face. But one could argue that joining the EU eliminated some of their sovereignty, as it linked each member nation at the hip economically (except for the UK which refused to use the Euro).
It might help to weather the storm by backing out of the EU, and lower the amount of imports for a few years. It will not make things better short term, but increased reliance on domestic goods (provided they have the ability to make them) could help to at least get back to neutral ground. That is the first step on their road to recovery.
As much as it would hurt them, cutting back on the woefully excessive social services may be another option. There was no way they could sustain such an expense; lying just made it worse.