A monitoring module selectively generates a request to at least one of: transition from providing rich fueling an engine to operating the engine in a fuel cutoff (FCO) state; and transition from operating the engine in the FCO state to providing rich fueling to the engine. In response to a response to the request, the monitoring module: selectively controls fueling to the engine to perform the at least one of the transitions; and selectively determines whether a fault is present in a component based on a response to the at least one of the transitions. A hybrid control module controls an electric motor of the hybrid vehicle and that selectively generates the response.