Several theories of territorial rights argue that whenever possession of a particular territory is pivotal for sustaining established ways of life, the persons for whom that life is immensely important are entitled to control that territory. Life plans-based claims typically outweigh the competing claims of outsiders, except when urgent interests in human rights provision is at stake – in which case rights of refuge outweigh the territorial right of border control. I argue, against current presumption, that the weight of life plans-based claims is dramatically reduced over time. The citizens of existing states have a duty to gradually modify their way of life on the state’s territory whenever this is necessary for satisfying the claims of deprived outsiders (e.g. environmental refugees). This duty exists even when the outsiders’ claims are less-than-urgent; and we assume (arguendo) that the insiders’ claims prevail at the moment when the less-than-urgent-claims are first presented.