In Hermitian systems, according to the bulk–edge correspondence, interfacing two topological optical media with different bulk topological numbers implies the existence of edge states, which can trap light at the interface. However, such a general scenario can be violated when dealing with non-Hermitian systems. Here we show that interfacing two semi-infinite Hatano–Nelson chains with different bulk topological numbers can result in the existence of infinitely many edge (interface) states; however, light waves cannot be rather generally trapped at the interface