It was recently highlighted that nonreciprocal surface waves can be stopped in suitably designed waveguides, leading to the formation of hotspots wherein the electromagnetic fields are massively enhanced. Here, we prove that this phenomenon has a topological origin and is related to a breakdown of the bulk-edge correspondence in electromagnetic continua with no spatial cut-off. Our theoretical analysis shows that nonreciprocal electromagnetic continua can used to realize energy sinks with ultra-singular fields that absorb all the energy generated in their surroundings. Moreover, it is proven that similar energy sinks may be formed in fully reciprocal optical platforms with a parity-time-duality ( P∙T∙D ) symmetry.