Economic sanctions are widely used to pressure authoritarian regimes, yet their effectiveness remains contested. This paper shows that sanctions can inadvertently strengthen autocrats by accelerating the exit of their opponents. I develop a formal model in which sanctions deepen economic hardship, disproportionately affecting regime opponents and increasing their incentives to emigrate. I test the model using rich administrative data from Venezuela, tracking formal labor exits and electoral behavior before and after sanctions. Across multiple measures of pre-sanctions opposition strength, I find that opposition-aligned individuals and areas suffered larger labor market losses, likely reflecting selective emigration. Electoral precincts previously loyal to the opposition exhibited sharper declines in turnout and disproportionate increases in support for the regime. Rather than weakening Maduro, sanctions shifted the domestic political balance in his favor by hollowing out the opposition from below.