This paper develops a new cooperative jamming protocol, termed accumulate-and-jam (AnJ), to improve physical layer security in wireless communications. Specifically, a full-duplex (FD) friendly jammer is deployed to secure the direct communication between source and destination in the presence of a passive eavesdropper. We consider the friendly jammer as an energy-constrained node without embedded power supply but with an energy harvesting unit and rechargeable energy storage; it can thus harvest energy from the radio frequency (RF) signals transmitted by the source, accumulate the energy in its battery, and then use this energy to perform cooperative jamming. In the proposed AnJ protocol, based on the energy status of the jammer and the channel state of source-destination link, the system operates in either dedicated energy harvesting (DEH) or opportunistic energy harvesting (OEH) mode. Thanks to the FD capability, the jammer also harvests energy from the information-bearing signal that it overhears from the source. We study the complex energy accumulation and consumption procedure at the jammer by considering a practical finite-capacity energy storage, of which the long-term stationary distribution is characterized through applying a discrete-state Markov Chain. An alternative energy storage with infinite capacity is also studied to serve as an upper bound. We further derive closed-form expressions for two secrecy metrics, i.e., secrecy outage probability and probability of positive secrecy capacity. In addition, the impact of imperfect channel state information on the performance of our proposed protocol is also investigated. Numerical results validate all theoretical analyses and reveal the merits of the proposed AnJ protocol over its half-duplex counterpart.