Th EU is in big trouble. It would fall to the largest countries to sort this out, especially countries like Germany and France. The EU is quite unstable and it seems they have issue every few years. So just like in life it is the richest people who get to push their weight around and Germany and France have the most to gain. Smaller countries should be helped especially Greece as they simply do not have the resources to police their borders.
They allow anyone to join and sign their treaty in order to join. The EU high court still has to agree to it but they haven't stopped many countries. This means that many "poorer" countries were accepted into the EU, causing problems to it. (as the population of these countries could travel from a poorer country to a richer country for a better quality of life!)