Personalized medicine aims at tailoring treatment to the individual person through the sourcing of multiple health data from the population. The realization of these ambitions rest on the ability to reuse health data. But what does it take to reuse tissue and data collected from individuals in connection with treatment, for future purposes? It takes an "enabling public" consisting of not only people providing tissue and data, but also clinicians, researchers, and civil servants. Based on fieldwork and interviews from Denmark, we investigate how use attaches tissue and data to various actors in the enabling public. We argue that multiple forms of attachments and detachments co-exist and that these persist over time. Attentiveness to the character and coexistence of these attachments is crucial in discussions of the role different actors should play in the governance of tissue and data.