Accident anticipation aims to predict impending collisions from dashcam videos and trigger early alerts. Existing methods rely on binary supervision with manually annotated "anomaly onset" frames, which are subjective and inconsistent, leading to inaccurate risk estimation. In contrast, we propose RiskProp, a novel collision-anchored self-supervised risk propagation paradigm for early accident anticipation, which removes the need for anomaly onset annotations and leverages only the reliably annotated collision frame. RiskProp models temporal risk evolution through two observation-driven losses: first, since future frames contain more definitive evidence of an impending accident, we introduce a future-frame regularization loss that uses the model's next-frame prediction as a soft target to supervise the current frame, enabling backward propagation of risk signals; second, inspired by the empirical trend of rising risk before accidents, we design an adaptive monotonic constraint to encourage a non-decreasing progression over time. Experiments on CAP and Nexar demonstrate that RiskProp achieves state-of-the-art performance and produces smoother, more discriminative risk curves, improving both early anticipation and interpretability.