The article engages with biometric data gathering technologies as part of migration infrastructures for the monitoring and control of migration. It explores power and agency by paying attention to the complexity of readings, interpretations, and storytelling of illegalised migrants in the Moria and Kara Tepe camps, in the Island of Lesvos in Greece, as they received their bureaucratic legal papers and discussed developments in their ‘cases’. Borrowing from feminist and feminist security studies scholarship, the article argues for an understanding of data gathering and sharing infrastructures as material. It suggests that the datafication of migrants’ bodies constitutes a manifestation of power that ‘enacts’ the migrant body as a subject of power but also produces counter self-subjectifications. The article also suggests an understanding of subject agency as the ‘capacity to act’ within contexts of power. Such a position on the agency of illegalised migrants allows us to examine the emergence of solidarities and alliances and to understand and contextualise not only actions that seem to be questioning and rejecting power, but also those that accept it and internalise it as a strategy of survival and of bettering one’s life chances.