This work focuses on data-based fault detection and isolation (FDI) of nonlinear process systems. Working within the framework of controller-enhanced fault detection and isolation that we recently introduced, we address and solve an unresolved, practical problem. We consider the case where only output measurements are available and design appropriate state estimator-based output feedback controllers to achieve controller-enhanced fault detection and isolation in the closed-loop system. The necessary conditions for achieving fault detection and isolation using output feedback control are provided. We use a nonlinear chemical process example to demonstrate the applicability and effectiveness of the proposed method.