Understanding the labor market participation shift associated with an aging population and the challenges of employees who provide care to old-age relatives is essential to ensure progress toward the Sustainable Development Goals. The current study focuses on the decision of employees who combine paid work with unpaid care to relatives aged 65 and above to stay or leave their jobs. We draw on the Turnover Model and the Informal Caregivers Integrative Model (ICIM) to examine how two primary stressors—care burden and work demand—one secondary stressor—work–family conflict—and emotional exhaustion increase the turnover intentions of employees who combine paid work with eldercare to their old relatives aged 65 and over. By synthesizing these two models and using a survey with three chronological waves among 356 Israeli employees, we analyze a mediation model within a Structural Equation Modeling framework. The findings underscore the fact that work–family conflict (a secondary stressor) and the sense of exhaustion act as key mediators in the relationship between employees’ primary stressors and turnover intentions. The presence of primary stressors in themselves does not increase turnover intentions. Our findings imply that, rather than providing sporadic adaptations at work, policymakers, organizations, and human resource management systems should respond proactively to prevent the process from undermining employees’ ability to achieve equilibrium between their desire to work and care for their old-age relatives. Such a proactive stance would reduce their exhaustion and turnover intention.