When a subordinate state in a federal monetary union has severe fiscal problems and runs out of money, what does it do? It issues IOUs. Think California or the Argentine provinces before 2000. For example, in Portugal, we could coin a phrase and call such IOUs escudo. Essentially the government passes a decree that states that such escudo IOUs would be acceptable for all internal payments, except tax payments, between Portuguese residents, but not for any external payments between Portuguese residents and foreign residents. All public sector and private sector wage payments shift on to an escudo basis as do interest payments by a Portuguese resident to another resident. Portuguese residents’ deposits and borrowing with Portuguese banks shift to an escudo basis; others remain in euros.
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Note that the government, whose taxes remain paid in euro, would be long in euro, whereas the Portuguese private sector would be long escudo, short euro. So, the government transfers its net long to the central bank and asks the central bank to manage the escudo/euro exchange rate, so that it is stabilised, say at a level that represents a 25 per cent internal devaluation, (the choice of number would need careful calculation).
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It would be messy, and an unattractive dual currency mechanism. But it could work; it has done so before now in other countries and circumstances.