Simulating patients with large language models (LLMs) is a promising tool for mental health training, but existing approaches fail to capture a key clinical reality: self-stigma. Patients experiencing self-stigma, the internalization of negative stereotypes, often exhibit context-sensitive resistance, such as avoidance, denial, or self-blame, which current models render as static or uniformly compliant behavior. To address this, we introduce a novel simulation framework grounded in the psychological 3A1H model of self-stigmatization. Our core innovation is the creation of a \textbf{Stigmatized Self-Reflection} (\textbf{SSR}) dataset, where we augment mental health dialogues with internal monologues that reflect stigma-aware reasoning. By fine-tuning LLMs with this data using a chain-of-thought approach, we train patient agents to dynamically adjust their level and expression of stigma based on conversational triggers. Evaluations demonstrate that our approach significantly outperforms specialized baselines, generating more authentic and situationally appropriate patient responses. This work provides a crucial step towards realistic stigma simulation for clinical training and empathetic dialogue systems.