Any local change in supply chains will affect the overall performance. An accurate performance evaluation of the system is the basis to deal with the risk of chain break and improve its stability. Through a review of three types of common performance measures, it is pointed out that the existing measures are not suitable for supply chains under the risk of chain break. On the basis of distinguishing the impacts of intermediate products and export-oriented outputs on the upstream performance, a new performance measure for supply chains is proposed and its effectiveness in identifying broken chains is demonstrated. Based on the new measure, the distribution of supply chain performance is further discussed. By establishing safety stocks in response to the risk of chain break, how the upstream and downstream realize benefit sharing is investigated. Nash bargaining method is employed to analyze the performance decomposition in the centralized system and the performance negotiation in the decentralized system. It is shown that the decentralized supply chain can achieve the centralized optimality through Nash bargaining. An illustrative example further verifies the relevant conclusions. The results show that the setting of safety stocks can prevent the upstream performance from declining to zero due to chain break, and meanwhile it can improve the downstream performance so as to enhance the stability of demands.