This work examines the impact of local losses produced by a resistive wiremesh on the modes of an acoustic cavity. In the 1D case, we demonstrate the ability to selectively affect the modes, ranging from being completely unaffected by the wiremesh to being fully absorbed by it. This effect can be used to filter the cavity modes. In the 2D case, we discuss the effect of wiremesh rotation on the cavity modes. A new type of modes that are localized on the wiremesh with a purely imaginary eigenfrequency has been identified. These findings show that wiremeshes are ultrabroadband lossy metasurfaces offering a simple and straightforward way to explore passive non-Hermitian systems.