Inappropriate design and deployment of machine learning (ML) systems lead to negative downstream social and ethical impacts -- described here as social and ethical risks -- for users, society, and the environment. Despite the growing need to regulate ML systems, current processes for assessing and mitigating risks are disjointed and inconsistent. We interviewed 30 industry practitioners on their current social and ethical risk management practices and collected their first reactions on adapting safety engineering frameworks into their practice -- namely, System Theoretic Process Analysis (STPA) and Failure Mode and Effects Analysis (FMEA). Our findings suggest STPA/FMEA can provide an appropriate structure for social and ethical risk assessment and mitigation processes. However, we also find nontrivial challenges in integrating such frameworks in the fast-paced culture of the ML industry. We call on the CHI community to strengthen existing frameworks and assess their efficacy, ensuring that ML systems are safer for all people.