FORTUNE — Bank runs typically spell financial disaster. Any responsible government would try to avoid one, but Greece could turn out to be a special case. If everyone pulled their money out from Greek banks, that might actually save the debt-ridden country from leaving the Euro.  The advice, albeit unusual, comes from Peterson Institute for International Economics’ Jacob Funk Kirkegaard. In a research note released last week, Kirkegaard spells out how a speedier bank run might finally give voters the wake-up call they need.  Next month, Greece will have a national election after the May election failed to produce a clear winner. However, voters did show relatively strong support for anti-austerity party Syriza led by Alexis Tsipras – what many view as a troubling development. If the new government reneges on Greece’s austerity pledges, the IMF and the European Union could cut off the flow of bailout loans – which, for the past two years, have largely kept Greece afloat from bankruptcy.  MORE: No, Facebook did not make Bono world’s richest musician  Greece’s problems have roiled global markets, but it has done little to sway voters who have met austerity measures with street riots. They refuse to see that Greece can’t go on without agreeing to deep spending cuts supported by the International Monetary Fund. Might a bank run do the trick? Admittedly, Kirkegaard’s suggestion should come with a big warning label – something he even acknowledges.  But his urging for a bank run is worth attention, to the extent that it leads to a broader question: How bad do things have to get before Greeks realize they need to spend way less?  To be sure, there’s been a bank run in Greece for the past three years, as The Atlantic recently pointed out. Greek banks have lost between 25% and 30% of their deposits in what many have called a “bank jog” rather than a bank run. Greece’s worsening finances have led to a political crisis, and it remains to be seen if that will accelerate withdrawals from banks.  If the pace sped up, Kirkegaard thinks that might be the secret sauce to save the euro, as it would essentially discredit anti-austerity parties. That’s because the ECB would probably be tapped to make up for the lost deposits. It wouldn’t be in the interest for the central bank to see a collapse of Greece’s banking system and the ripple effects across Europe and possibly the rest of the world. So the ECB would probably feel pressured to rescue Greece but not without getting the country to sign up for the IMF program or perhaps scrap the elections and form a unity of technocratic government.  So maybe a bank run is the bitter medicine Greece needs. Of course, that may be easier said than done. As Slate’s Matthew Yglesias has pointed out, perhaps one reason why it appears more capital isn’t fleeing Greece is because the rise of direct deposits has made old-fashion bank runs “a bit more logistically difficult.”  Indeed, there are plenty of moving variables here. And in the coming months, it will be interesting to see what might finally make Greece face its debilitating debt.
Do the Greeks need bitter medicine? Pushing the economically ailing country's banks to the brink might be just what it takes to get austerity measures in place.