Is it possible to sustain an ambitious and redistributive Nordic welfare state in a Europe with open borders? Drawing on longitudinal administrative records spanning four decades, we first present discouraging historical evidence showing that labor migrants from low-income source countries tend to have unstable employment careers with marked overrepresentation in welfare programs. This pattern extends to post-accession labor migrants from Eastern Europe, who quickly experience high rates of unemployment. The article discusses possible avenues for making the welfare state "migration robust." We argue that there are alternatives to reclosing borders and/or cutting down welfare state ambitions, and recommend policies based on strengthening of activity requirements in social insurance programs, raising minimum job standards, and substitution of work-oriented services for cash-based family allowances.