The growing asymmetry in the size of fiscal imbalances poses a serious challenge to the macroeconomic stability of the Euro Area (EA). We show that following a contractionary shock, the current monetary and fiscal framework weakens economic growth even in low-debt countries because of the zero lower bound (ZLB) constraint. At the same time, the current framework also exposes the EA to the risk of fiscal stagflation if one country were to refuse to implement the necessary fiscal consolidations. We study a new framework that allows EA policymakers to separate the need for short-run macroeconomic stabilization from the issue of long-run fiscal sustainability. Following a contractionary shock, the central bank tolerates the increase in inflation needed to stabilize the amount of Eurobonds issued in response to a large EA recession. National governments remain responsible to back their country-level debt by fiscal adjustments. The policy acts as an automatic stabilizer that benefits both high-debt and low-debt countries, generating a moderate increase in inflation that mitigates the recession and allows the central bank to move away from the ZLB. At the same time, the proposed policy lowers the risk of fiscal stagflation because it endows EA countries with effective stabilization policies.