This paper introduces the concept of wireless-powered zero-energy reconfigurable intelligent surface (zeRIS), and investigates a wireless-powered zeRIS aided communication system in terms of security, reliability and energy efficiency. In particular, we propose three new wireless-powered zeRIS modes: 1) in mode-I, N reconfigurable reflecting elements are adjusted to the optimal phase shift design of information user to maximize the reliability of the system; 2) in mode-II, N reconfigurable reflecting elements are adjusted to the optimal phase shift design of cooperative jamming user to maximize the security of the system; 3) in mode-III, N1 and N2 (N1+N2=N) reconfigurable reflecting elements are respectively adjusted to the optimal phase shift designs of information user and cooperative jamming user to balance the reliability and security of the system. Then, we propose three new metrics, i.e., joint outage probability (JOP), joint intercept probability (JIP), and secrecy energy efficiency (SEE), and analyze their closed-form expressions in three modes, respectively. The results show that under high transmission power, all the diversity gains of three modes are 1, and the JOPs of mode-I, mode-II and mode-III are improved by increasing the number of zeRIS elements, which are related to N2, N, and N^2_1, respectively. In addition, mode-I achieves the best JOP, while mode-II achieves the best JIP among three modes. We exploit two security-reliability trade-off (SRT) metrics, i.e., JOP versus JIP, and normalized joint intercept and outage probability (JIOP), to reveal the SRT performance of the proposed three modes. It is obtained that mode-II outperforms the other two modes in the JOP versus JIP, while mode-III and mode-II achieve the best performance of normalized JIOP at low and high transmission power, respectively.