This article aimed to investigate the understanding of the need for care for mental illness among newly arrived refugees and asylum seekers in Sweden during 1990–2021. The article applied a crisis narrative perspective to contextualise why and how changes in legislation occur and the understanding of it. The article investigated how this is described and understood in legal texts, propositions, public investigations, and reports from 1990 to 2021 with an analytical frame of a crisis narrative through testimonies by journalists, professors linked to migration, a social worker, and a deputy principal. This will be understood from the theoretical perspectives of who has the right to have rights (Arendt, 2017) and who is grievable (Butler, 2016), as well as a holistic perspective on health. This article asks: (1) How have shifts in the documents about the right to health and perceptions of need for care among refugees and asylum seekers evolved over the time 1990–2021? And (2) What implications might the concepts of the “right to have rights” and being “grievable” have for the health of refugees and asylum seekers? A qualitative thematic document analysis was adopted with an exploratory design based on an inductive approach to the empirical material. I argue that the legal texts, propositions, public investigations, and reports have shifted towards a more decentralised structure with a more holistic perspective on health. Together with the witness seminars, this testifies that, paradoxically, the shift has led to a more individualised view of refugees and asylum seekers who take responsibility for their health to a greater extent, where the uncertainty of residence permits is linked to an insecure and precarious existence. © The Author(s) 2025.