We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry-related spatial domains. Using experimental data, we verify this mapping with remarkable accuracy. For the performed experiment, we employ a construction technique based on local symmetries that allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains, and they clearly indicate that completely locally symmetric devices constitute a promising class of setups with regard to the manipulation of wave propagation.