The European Central Bank has already declared that they won't let any of their member states go under, which means they are committed to printing as much money as needed....
Mario Draghi said, "Within our mandate, the ECB is ready to do whatever it takes to preserve the euro. And believe me, it will be enough."
Financing a member state via printing money does not exist within the ECB's mandate. So the ECB cannot legally do what you say they are doing. Greece is financing itself via ELA Emergency Liquidity Assistance, where Greek banks loan the Greek government money that cannot be repaid, then the ELA rescues the Greek banks from the bad loans. This type of back-door financing is not sustainable and will eventuall collapse under its own weight. OTOH, the ECB also lacks the mandate to kick a member state out of the common currency when they are unwilling and unable to meet the conditions for membership. Only the political leadership of the member states have the authority to either change the ECB's mandate, or to kick a member state out. How this will turn out is anybody's guess.