Scholars across Computer-Supported Cooperative Work (CSCW) increasingly focus on the topic of care when investigating data-driven technologies in contexts of re-humanizing technology design and usage. Previous studies have shown how care work eludes complex bureaucratic systems shaped by data, digitalization, and a restrictive political agenda. This research aims to understand how asylum stakeholders enact care as an aspect of asylum casework, while navigating what is largely acknowledged by NGOs, nation states, and the EU to be a broken asylum system (von der Leyen). We investigate care as a relational aspect of casework in which knowledge and technology of the implicated caseworker and asylum seeker are attuned to one another in a way that takes the unaccountable into account (following Mol 2010). We add to studies of care in CSCW by empirically expanding the research sites of care and data work. In this multi-sited ethnographically informed study, we conducted interviews (n = 19) and 160 h of observational studies amongst: 1) Danish Red Cross care workers; 2) Danish Refugee Council legal counsellors; and 3) Danish Immigration Service case officers. We contribute empirically grounded insights into the meanings of care in a datafied asylum context. We find that care is enacted by caseworkers in moments of ambivalence, translation, and attentiveness to “new substantial information” relevant for asylum decision-making. We find that these relational aspects of care in asylum casework impact the production of data about the asylum seeker. We end with a discussion of how a care perspective increases our sensitivity as CSCW researchers towards understanding the conditions for producing quality data and documentation in casework.