Traditional wireless communication transmission and network access rely on radio frequency (RF) communication technologies. With the influx of massive mobile devices into the network, the problems such as spectrum scarcity and energy constraint pose challenges to the sustainable development of the new generation Internet-of-Things (IoT). Through the integration of traditional RF communication technology and emerging visible light communication (VLC) technology, an efficient and robust hybrid VLC/RF cooperative communication system with simultaneous lightwave information and power transfer (SLIPT) was proposed. To bridge the light-emitting diode (LED) source and the destination far away, an off-the-grid relay that can move randomly within source coverage was introduced. The end-to-end link could be divided into two hops (i.e. VLC link and RF link) through relay forwarding. Specifically, in the 1st hop, the optical signal received at the relay was separated into alternating current and direct current components for information decoding and energy harvesting respectively. Then, the harvested energy was used to forward the decoded source information to the destination by using RF in the 2nd hop. Considering the constraints imposed by the average power and peak power on the LED source, the distinct channel conditions across the two hops, the relay location, signal processing, and the energy harvested by the relay were taken into account in this study. On this basis, the end-to-end outage probability, data throughput, and energy efficiency of the system were analytically derived in closed-form expressions. Simulation results demonstrate that with proper parameter configurations, a balance could be reached between the transmission performances of the two hops. The proposed method could effectively promote the matching between the information flow and the energy flow in the system, thus significantly improving the reliability, throughput, and energy efficiency of the system.