Dark sectors are well-motivated extensions of the Standard Model that can explain the existence of dark mater. These scenarios generically feature feebly coupled, light new particles that are difficult let to constrain with current high-energy colliders. Instead, high intensity experiments offer the best chance to probe light dark sector particles. In this talk, we will discuss the possibility of probing dark sectors with beam dump experiments at future high energy lepton colliders. In particular, experiments like the International Linear Collider or a Muon Collider feature both high intensity and high energy beams, which can probe large regions of parameter space of dark sector models. Focusing on heavy neutral leptons as a benchmark model, we show these experiments can probe new regions of parameter space, and are complementary to other proposed experiments such as proton beam dump experiments, neutrino experiments, and LHC auxiliary detectors.