The subjectivities that shape data collection and management have received extensive criticism, especially with regards to the digitization projects and digital archives of galleries, libraries, archives and museums (GLAM institutions). The role of digital methods for recovering data absences is increasingly receiving attention too. Conceptualizing the absence of non-hegemonic individuals from the catalogues of Sir Hans Sloane as an instance of textual haunting, this article will ask: to what extent do data-driven approaches further entrench archival absences and silences? Can digital approaches be used to highlight or recover absent data? This article will give a decisive overview of relevant literature and projects so as to examine how digital tools are being realigned to recover, or more modestly acknowledge, the vast, undocumented network of individuals who have been omitted from canonical histories. Drawing on the example of Sloane, this article will reiterate the importance of a more rigorous ethics of digital practice, and propose recommendations for the management and representation of historical data, so cultural heritage institutions and digital humanists may better inform users of the absences and subjectivities that shape digital datasets and archives. This article is built on a comprehensive survey of digital humanities’ current algorithmic approaches to absence and bias. It also presents reflections on how we, the authors, grappled with unforeseen questions of absence and bias during a Leverhulme-funded collaboration between the British Museum and University College London (UCL), entitled ‘Enlightenment Architectures: Sir Hans Sloane’s Catalogues of his collections’.