  Context: We present a newly discovered class of low-luminosity, dusty,
evolved objects in the Magellanic Clouds. These objects have dust excesses,
stellar parameters, and spectral energy distributions similar to those of dusty
post-asymptotic giant branch (post-AGB) stars. However, they have lower
luminosities and hence lower masses. We suggest that they have evolved off the
red giant branch (RGB) instead of the AGB as a result of binary interaction.
Aims: In this study we aim to place these objects in an evolutionary context
and establish an evolutionary connection between RGB binaries (such as the
sequence E variables) and our new sample of objects. Methods: We compared the
theoretically predicted birthrates of the progeny of RGB binaries to the
observational birthrates of the new sample of objects. Results: We find that
there is order-of-magnitude agreement between the observed and predicted
birthrates of post-RGB stars. The sources of uncertainty in the birthrates are
discussed; the most important sources are probably the observational
incompleteness factor and the post-RGB evolution rates. We also note that
mergers are relatively common low on the RGB and that stars low on the RGB with
mid-IR excesses may recently have undergone a merger. Conclusions: Our sample
of dusty post-RGB stars most likely provides the first observational evidence
for a newly discovered phase in binary evolution: post-RGB binaries with
circumstellar dust.
