This chapter examines the political struggle over access to emergency medical treatment for asylum seekers and refugees in Australia’s offshore processing facilities. The Australian government’s efforts to deny people critical medical care have been criticised as a breach of human rights obligations. The plight of individuals sent offshore is viewed through the lens of Arendt’s work on the dangerous precarity of displaced people. The denial of healthcare to refugees and asylum seekers, the chapter argues, is a function of a more fundamental denial. In keeping asylum seekers outside the boundary within which an effective rights claim can be raised, offshore processing is a strategy for depriving asylum seekers of the right to have rights.