A promising application of unmanned aerial vehicles (UAVs) to the future communication networks is to address emergency communications. This paper considers such a scenario where a UAV is employed to a malfunction area (modeled as a circular disc) in which all ground base stations (BSs) break down. The ground BSs outside the malfunction area are modelled as a homogeneous Poisson point process (HPPP). Particularly, a user-centric cooperative scheme is proposed to serve the UEs in the 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. The region size of each type can be adjusted by a cooperation parameter $\delta$. Through rigorous derivations, an expression for the coverage probability achieved by the UE in the malfunction area is obtained. In order to provide a fair comparison, the normalized spectral efficiency (NSE) which is defined by taking both system throughput and the number of serving BSs into consideration, is used as a criterion for the performance evaluation. Numerical results are presented to verify the accuracy of the analytical results and also to demonstrate the superior performance of the proposed scheme.