There are two silly options. One, they can sue all modern countries for patent infringement on concepts like democracy and philosophy. Two, they could continue to make the attempt to pay down their debt, something that might require paying about 20% of GDP per year. Both possible but wildly improbable.
Before I make my simple suggestion for how to resolve this, let me tell you what I'm not whining about. I'm not whining about the fact that my portfolio has taken a serious hit. Again. Also, my house has dropped a huge amount in the last few years. Because of fluctuations in housing and stock markets, my net worth has dropped by tens of percent. I wish this hadn't happened but you know what? This is what it means to invest. You accept risk in return for ... well, for returns. You don't whine about the loss. You don't demand that some bank or company give you money for what your house or stocks were once worth. You accept the lose and move on. Why is it that we think bond investors should be exempt from this reality of investing?
So, Greece cannot pay back its debt. Why not write it down? Why not pay off half or less? Investors will lose money, of course. Join the club.
Will this create problems? Yes. Every solution will. But the sooner debt is written off, the sooner the Greek government can begin with something short of radical contractions in spending that risk triggering a recession or even depression.