There is wide concern that migration flows may undermine the financial viability of generous welfare arrangements. The discussion focuses on welfare arrangements as attractors of migrants, suggesting that the issue does not pertain to migrant workers. However, this overlooks how welfare arrangements affect return-migration in case of social events like job loss. Importantly, migrants are shown to be self-selected in a way affecting both migration and return-migration. Two migration regimes prevail. In one, with relatively low benefits, unemployed workers return, while in the other some stay. Importantly, the stay or return migration decision is more sensitive to welfare generosity than the migration decision.