Serious illness communication (SIC) in end-of-life care faces challenges such as emotional stress, cultural barriers, and balancing hope with honesty. Despite its importance, one of the few available ways for clinicians to practice SIC is with standardized patients, which is expensive, time-consuming, and inflexible. In this paper, we present SOPHIE, an AI-powered standardized patient simulation and automated feedback system. SOPHIE combines large language models (LLMs), a lifelike virtual avatar, and automated, personalized feedback based on clinical literature to provide remote, on-demand SIC training. In a randomized control study with healthcare students and professionals, SOPHIE users demonstrated significant improvement across three critical SIC domains: Empathize, Be Explicit, and Empower. These results suggest that AI-driven tools can enhance complex interpersonal communication skills, offering scalable, accessible solutions to address a critical gap in clinician education.