In causal inference literature, potential outcomes are often indexed by the "elimination of all right-censoring events," leading to the perception that such a restriction is necessary for defining well-posed causal estimands. In this paper, we clarify that this restriction is not required: a well-defined estimand can be formulated without indexing on the elimination of such events. Achieving this requires a more precise classification of right-censoring events than has historically been considered, as the nature of these events has direct implications for identification of the target estimand. We provide a framework that distinguishes different types of right-censoring events from a causal perspective, and demonstrate how this framework relates to censoring definitions and assumptions in classical survival analysis literature. By bridging these perspectives, we provide a clearer understanding of how to handle right-censoring events and provide guidance for identifying causal estimands when right-censored events are present.