Fluorescence microscopy offers unparalleled access to the spatial organization and dynamics of biological events in living samples, yet capturing rare processes over extended durations remains challenging due to trade-offs between exposure to excitation light and sample health. Here, we introduce hybrid-EDA, an event-driven acquisition (EDA) framework that combines the gentleness and contextual richness of phase-contrast with the functional specificity of fluorescence. We develop surveillance for events of interest in label-free microscopy using dynamics-informed neural networks that trigger smart fluorescence acquisitions upon detection. This allows us to dramatically reduce phototoxic damage while obtaining specific and functional information from fluorescence when beneficial. We demonstrate how hybrid-EDA enables improved imaging acquisitions of organelle contacts and mitochondrial divisions. We envision that hybrid-EDA will enable insights into a range of dynamic and rare biological processes, providing a powerful and general strategy for cell-friendly imaging.