Due to disaster or other reasons, communication interruption may occur in malfunction areas where all ground base stations (BSs) break down. This paper intends to study the application of deploying unmanned aerial vehicle (UAV) to such a malfunction area for recovering communications. Particularly, the malfunction area is modeled as a disc, outside which the ground BSs can still work normally, and a user-centric cooperative scheme is proposed in this paper to serve the UEs in such a malfunction area. According to the user equipment's (UE's) connections to the UAV and the nearest ground BS, the malfunction area is divided into three regions, namely the UAV region, the cooperation region and the nearest ground BS region, in which the UEs are served by the UAV only, both the UAV and the nearest ground BS, and the nearest ground BS, respectively. By using tools from stochastic geometry, the distribution of the distance from a UE to its nearest ground BS and the laplace transform for the interference from the ground BSs farther than the nearest ground BS are characterized, which is more challenging compared to the conventional scenarios in which only terrestrial BSs are considered. Furthermore, an expression for the coverage probability achieved by a typical UE is obtained. In order to provide a fair comparison, the normalized spectral efficiency (NSE) is defined by taking both system throughput and the number of serving BSs into consideration. Numerical results are presented to verify the accuracy of the analytical results and also to demonstrate the superior performance of the proposed scheme.