Spain was able to break the sovereign/banking nexus by having the ESM bailout Spanish banks directly and leaving the sovereign out of the mix. Ireland, which went bust bailing out its over-leveraged banking system, wants the same deal. There has been lots of discussion along those lines but so far Ireland remains on the hook as a sovereign nation for the cost of the bailout.
If the ESM were to step in and recapitalize the banks, Ireland’s public finances would immediately recover to a very large degree. High social spending owing to unemployment will remain a drag on finances, of course.