Policies targeting disadvantaged areas aim to improve their conditions, but the labels they impose carry consequences of their own. In this paper, we examine Denmark's Ghetto Plan, one of the first recent place-based policies explicitly targeting migrant populations. Under this policy, certain public housing deemed problematic were officially designated as "ghettos", with minimal additional implications. Using rich administrative data and a Difference-in-Differences approach, we show that the policy backfired, worsening spatial inequality through compositional shifts driven by native avoidance. In addition, the policy was particularly detrimental to exposed natives, who accepted a 4% annual income loss to leave stigmatized areas.