  We show that the rainbow state, which has volume law entanglement entropy for
most choices of bipartitions, can be embedded in a many-body localized
spectrum. For a broad range of disorder strengths in the resulting model, we
numerically find a narrow window of highly entangled states in the spectrum,
embedded in a sea of area law entangled states. The construction hence embeds
mobility edges in many-body localized systems. This can be thought of as the
complement to many-body scars, an `inverted quantum many-body scar', providing
a further type of setting where the eigenstate thermalization hypothesis is
violated.
