This paper focuses on the problem of fault-tolerant control of spatially distributed systems modeled by parabolic PDEs with networked sensors and actuators and actuator faults. Based on a suitable finite-dimensional model that captures the dominant dynamics of the infinite-dimensional system, an event-triggered networked control system that enforces closed-loop stability with minimal sensor-controller communication is initially designed. The model is used by the controller to generate the necessary control action when communication is suspended, and its state is updated using the real-time measurements when communication is restored. Communication is triggered when a state-dependent threshold on the model estimation error is breached. The communication threshold is obtained using Lyapunov techniques and is explicitly characterized in terms of the fault magnitude, the model and controller design parameters, and the actuator locations. This characterization captures the potential impact of faults on both closed-loop stability and network resource utilization, and is used to devise stability-based and performance-based fault accommodation strategies that guarantee closed-loop stability and keep network resource utilization to a minimum in the presence of faults. Finally, the results are illustrated using a diffusion-reaction process example.