This paper focuses on the study of consensus-based information fusion for a team of sensors, where some of them are active, in directed networks when communication among sensors is directed. In the context of this paper, a sensor is called active if it can obtain information about certain objects while a sensor is called inactive if it cannot obtain information. Moreover, each sensor is able to determine if it is active or inactive. Although inactive sensors do not provide information, they are needed in order to maintain connectivity of the communication graph. Due to the existence of inactive sensors, the existing research on consensus-based information fusion for a team of active sensors cannot be applied. We first provide a mathematical formulation of consensus-based information fusion for both inactive and active sensors. Then we derive sufficient conditions to guarantee that all active and inactive sensors reach consensus on their final state information. In particular, we consider two different cases: (1) the existence of one inactive sensor, and (2) the existence of multiple inactive sensors. For the first case, we also show explicitly the final state information of all active sensors.