  We show that anomalous Floquet topological insulators generate intrinsic,
non-Hermitian topology on their boundary. As a consequence, removing a boundary
hopping from the time-evolution operator stops the propagation of chiral edge
modes, leading to a non-Hermitian skin effect. This does not occur in Floquet
Chern insulators, however, in which boundary modes continue propagating. The
non-Hermitian skin effect on the boundary is a consequence of the nontrivial
topology of the bulk Floquet operator, which we show by designing a real-space
topological invariant. Our work introduces a form of `mixed' higher-order
topology, providing a bridge between research on periodically-driven systems
and the study of non-Hermiticity. It suggests that periodic driving, which has
already been demonstrated in a wide range of experiments, may be used to
generate non-Hermitian skin effects.
