  One of the central ideas regarding anomalies in topological phases of matter
is that they imply the existence of higher-dimensional physics, with an anomaly
in a D-dimensional theory typically being cancelled by a bulk (D+1)-dimensional
symmetry-protected topological phase (SPT). We demonstrate that for some
topological phases with reflection symmetry, anomalies may actually be
cancelled by a D-dimensional SPT, provided that it comes embedded in an
otherwise trivial (D+1)-dimensional bulk. We illustrate this for the example of
$\mathbb{Z}_N$ topological order enriched with reflection symmetry in (2+1)D,
and along the way establish a classification of anomalous reflection symmetry
fractionalization patterns. In particular, we show that anomalies occur if and
only if both electric and magnetic quasiparticle excitations possess nontrivial
fractional reflection quantum numbers.
