In this article, it is experimentally verified that nonreciprocal photonic systems with a continuous translation symmetry may have an ill-defined topology. The topological classification of such systems is only feasible when the material response is regularized with a spatial-frequency cutoff. Here, we experimentally demonstrate that adjoining a small air layer to the relevant material interface may effectively imitate an idealized spatial cutoff that suppresses the nonreciprocal response for short wavelengths and regularizes the topology. Furthermore, it is experimentally verified that nonreciprocal systems with an ill-defined topology may be used to abruptly halt the energy flow in a unidirectional waveguide due to the violation of the bulk-edge correspondence. In particular, we report the formation of an energy sink that absorbs the incoming electromagnetic waves with a large field enhancement at the singularity.