With the rapid development of autonomous driving systems (ADSes), real-world roads are evolving into mixed-traffic environments where autonomous vehicles (AVs) and other traffic participants (e.g., human-driven vehicles (HDVs), cyclists, and pedestrians) coexist and interact with each other. However, current ADSes still incur various safety violations in mixed traffic scenarios, raising a strong demand for runtime safety assurance frameworks that can continuously monitor hazards and prevent potential violations. Existing ego-centric assurance approaches are insufficient for mixed traffic, where violations often arise from locally reasonable yet jointly incompatible decisions among multiple vehicles and cannot be reliably resolved through independent takeover. To bridge this gap, we propose CoSafe, a modular and ADS-agnostic cooperative runtime safety assurance framework for mixed-traffic autonomous driving to extend runtime safety assurance from ego-centric takeover to scene-level cooperative intervention. CoSafe leverages vehicle-to-everything (V2X) communication to enable roadside units (RSUs) to monitor scene-level hazards and jointly mitigate hazards involving multiple vehicles. We integrate CoSafe with seven state-of-the-art ADSes, and our evaluation on the InterDrive benchmark demonstrates that CoSafe improves the driving score of AVs by 70.03% on average, reduces safety violations by 87.80%, and accurately identifies unsafe AVs with an F3 score of 0.930, while satisfying real-time constraints.

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