Red-teaming, where adversarial prompts are crafted to expose harmful behaviors and assess risks, offers a dynamic approach to surfacing underlying stereotypical bias in large language models. Because such subtle harms are best recognized by those with lived experience, involving targets of stereotyping as red-teamers is essential. However, critical challenges remain in leveraging their lived experience for red-teaming while safeguarding psychological well-being. We conducted an empirical study of participatory red-teaming with 20 individuals stigmatized by stereotypes against nonprestigious college graduates in South Korea. Through mixed methods analysis, we found participants transformed experienced discrimination into strategic expertise for identifying biases, while facing psychological costs such as stress and negative reflections on group identity. Notably, red-team participation enhanced their sense of agency and empowerment through their role as guardians of the AI ecosystem. We discuss implications for designing participatory red-teaming that prioritizes both the ethical treatment and empowerment of stigmatized groups.