We analyze a union of financially-integrated yet politically-sovereign countries, where households in the Northern core of the union lend to those in the Southern periphery in a unified debt market subject to a borrowing constraint. This constraint generates sudden stops throughout the South, depresses the intra-union interest rate, and reduces Northern welfare below its unconstrained level, while having ambiguous effects on Southern welfare. During sudden stops, Pareto improvements can be achieved using North-to-South governmental loans if Southern governments have the capacity to commit to repay, or using a combination of Southern debt relief and budget-neutral taxes and subsidies if they do not. From the pre-crisis perspective, it is Pareto-improving to allow loans and debt relief to be negotiated in later sudden-stop periods as long as the regions in the union are sufficiently heterogeneous to begin with. We show that our results are robust to production and to limited financial openness of the union.