An emerging challenge for time-to-event data is studying semi-competing risks, namely when two event times are of interest: a non-terminal event time (e.g. age at disease diagnosis), and a terminal event time (e.g. age at death). The non-terminal event is observed only if it precedes the terminal event, which may occur before or after the non-terminal event. Studying treatment or intervention effects on the dual event times is complicated because for some units, the non-terminal event may occur under one treatment value but not under the other. Until recently, existing approaches (e.g., the survivor average causal effect) generally disregarded the time-to-event nature of both outcomes. More recent research focused on principal strata effects within time-varying populations under Bayesian approaches. In this paper, we propose alternative non time-varying estimands, based on a single stratification of the population. We present a novel assumption utilizing the time-to-event nature of the data, which is weaker than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present non-parametric and semi-parametric estimation methods for right-censored data.