Thousands of human remains are stored in museums and collections worldwide. But while their collection, handling and display are increasingly subjected to ethical guidelines and regulations, institutional guidelines and research on their digitization are scarce. This study explores the challenges and opportunities of digitizing human remains, outlining new directions. Based on interviews (n=23) with museum professionals across 14 organizations worldwide, we map: 1) A taxonomy of data work with human remains; 2) Main areas of uncertainties in data work and adaptive strategies currently employed to address them; 3) Examples of ill-fitting digital systems. We introduce the concept of ‘data hauntings’ to highlight the historical, technical and regulatory ghosts lingering in digital systems of contested assets, and the specters of future data circulation. Lastly, we propose a ‘hauntological’ framework for rethinking, (re)designing and maintaining digital systems to enable equitable data work - balancing historical trace-ability, ethical accountability and searchability.