Greece owes billions to the IMF and German banks, but does not have the means to pay it back. Hungary's solution to a similar problem was drastic, but might offer the Greeks a useable scenario. Hungary did not join the euro zone, but much Hungarian debt, public and private, was denominated in euros. When the debts spiraled higher in terms of forints, the Hungarian currency, the government stepped in to declare all debts were payable in forints--not exactly an outright default but it allowed the country to reduce the amount of debt in terms of its devalued domestic currency. Greece could unilaterally declare its debts payable in devalued drachmas without withdrawing from the EU and euros could still circulate. If Greece pursued this course, however, it might be thrown out of the union by irrate lenders.
Most Greeks want to remain united with the rest of Europe, but are fed up with foreign banker-imposed austerity. That is why they elected a socialist government. But if Greeks cannot pay their way, some countries want Greece out. The question of Greek survival in the EU has come down to whether an elected government in the cradle of democracy has any legitimacy left if its policies are to be dictated by foreign economic powers. The EU was built as a free trade zone that sould benefit all of its member states. The Greek national meltdown and German trade dominance has brought this underlying assumption into question.