Well the ECB could just print couple of trillion euro and hang them out divided to each country. We will have a little inflation and that's it. Greece will be debt free and there will be no burdens on the taxpayers.
https://www.theguardian.com/world/2015/jul/06/return-drachma...
These were, of course, indistinguishable from real notes. The scheme ultimately failed when a mistake caused the printing of duplicate serial numbers already ordered by the state.
I doubt a scheme like this would work today in the slightest. If in an un-digitized world this didn't last long, in today's world it would quickly be discovered.
In practice they could only start their own “unauthorised” printing if it was kept secret since if it leaked the ECB would just issue new notes. This would likely be highly disruptive to the ECB as it was to Portugal.