Any decision to stop ELA to Greek banks would be taken at the highest political level

There were many questions on Greece. The key message from President Draghi was that Eurosystem support for the Greek banking system through ELA will continue so long as banks are solvent and have adequate collateral. 

This, in turn, will depend on the capacity of the Greek government to complete the current programme review, as uncertainty continues to generate deposit outflows and worsens growth prospects, both of which work against the capital position and solvency of Greek banks. 

According to Barclays - "ELA assistance is critical to Greece remaining in the EMU but any decision to potentially stop ELA (which requires at least a two-thirds majority at the GC) would in all likelihood be taken at the highest political level, even it were to be executed by the ECB's GC."