Novel biological entities such as cell lines and organoids do not typically fit into established conceptual categories, such as 'human' or 'nonhuman', 'gift' or 'property'. This makes developing robust ethical principles or policy solutions difficult. In this article, we present a new approach to the ethics of novel biological entities, which we call 'liminal bioethics'. We argue that some entities are best understood as liminal; we should not try to shoehorn them into existing categories or modify our concepts to suit them. However, we must investigate which concepts help articulate an entity's liminal status most precisely. The choice of concepts, in turn, may suggest correspondingly liminal ethical principles or solutions for that entity. To demonstrate how this method works, we focus on immortalised cell lines as a test case, while also considering its implications for more recent breakthroughs in cell culture technology relating to organoids and assembloids. First, we demonstrate why the gift-property distinction is inadequate for framing the liminality of cell lines. We then argue for cell lines as being located in a liminal conceptual space between body part and organism, and discuss the conceptual shift that this entails for understanding the status of cell lines and organoids. We suggest that ethical principles in relation to cell lines should reflect this particular liminality; for example, commercial exchange of cell lines seems more acceptable than with body parts, but some means of respecting cell lines' continuing human connection should still be in place.