Anthropogenic climate change is an existential threat to the people of sinking island states. When their territories inevitably disappear, what, if anything, do the world's remaining territorial states owe them? According to a prominent ‘nationalist’ approach to territorial rights – which distributes such rights according to the patterns of attachment resulting from people's incorporation of particular territories into their ways of life – the islanders are merely entitled to immigrate, not to reestablish territorial sovereignty. Even GHG-emitting collectives have no reparative duty to cede territory, as the costs of upsetting their territorial attachments are unreasonable to impose, even on wrongdoers. As long as they allow climate refugees to immigrate, receiving countries have done their duty, or so the nationalist argues. In this article, I demonstrate that the nationalist's alleged distributive equilibrium is unstable. When the islanders lay claim to new territory, responsible collectives have a duty to modify their way of life – gradually downsizing their territorial attachments – such that the islanders, in time, may receive a new suitable territory. Importantly, by deriving this duty from the nationalist's own moral commitments, I discard the traditional assumption that nationalist premises imply a restrictive view on what we owe climate refugees.