Two-hop relay wireless network serves as an important network model for the performance study of general wireless networks, while cooperative jamming has been a promising physical layer approach to providing a strong form of security. This work focuses on exploring eavesdropper-tolerance capability, namely, the maximum number of eavesdroppers that can be tolerated to ensure the desired level of security and reliability, in two-hop relay wireless networks via cooperative jamming scheme. While previous works on this problem studied either the scaling law results for infinite networks or corresponding bounds for finite networks, this paper derives the exact maximum number of eavesdroppers that can be tolerated for networks with finite number of system nodes. To the best of our knowledge, this is the first work concerning the study of exact eavesdropper-tolerance capability for wireless networks. Extensive simulations and numerical studies are then conducted to verify the efficiency of our theoretical models and to explore the inherent performance tradeoffs between the eavesdropper-tolerance capability and security/reliability constraints.