Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth two-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in discontinuous maps. These pseudo-boundaries originate in groups of chains of islands which separate parts of the phase space and need to be crossed in order to move between the different subspaces. Trajectories, however, do not easily cross these chains, but tend to propagate along them. This type of behaviour is demonstrated by using a 'generalized' Fermi map.