A primary objective of the forthcoming sixth generation (6G) of wireless networking is to support demanding applications, while ensuring energy efficiency. Programmable wireless environments (PWEs) have emerged as a promising solution, leveraging reconfigurable intelligent surfaces (RISs), to control wireless propagation and deliver exceptional quality-ofservice. In this paper, we analyze the performance of a network supported by zero-energy RISs (zeRISs), which harvest energy for their operation and contribute to the realization of PWEs. Specifically, we investigate joint energy-data rate outage probability and the energy efficiency of a zeRIS-assisted communication system by employing three harvest-and-reflect (HaR) methods, i) power splitting, ii) time switching, and iii) element splitting. Furthermore, we consider two zeRIS deployment strategies, namely BS-side zeRIS and UE-side zeRIS. Simulation results validate the provided analysis and examine which HaR method performs better depending on the zeRIS placement. Finally, valuable insights and conclusions for the performance of zeRISassisted wireless networks are drawn from the presented results.