  Modelling dust formation in single stars evolving through the carbon-star
stage of the asymptotic giant branch (AGB) reproduces well the mid-infrared
colours and magnitudes of most of the C-rich sources in the Large Magellanic
Cloud (LMC), apart from a small subset of extremely red objects (EROs). The
analysis of EROs spectral energy distribution suggests the presence of large
quantities of dust, which demand gas densities in the outflow significantly
higher than expected from theoretical modelling. We propose that binary
interaction mechanisms that involve common envelope (CE) evolution could be a
possible explanation for these peculiar stars; the CE phase is favoured by the
rapid growth of the stellar radius occurring after C$/$O overcomes unity. Our
modelling of the dust provides results consistent with the observations for
mass-loss rates $\dot M \sim 5\times 10^{-4}~\dot M/$yr, a lower limit to the
rapid loss of the envelope experienced in the CE phase. We propose that EROs
could possibly hide binaries of orbital periods $\sim$days and are likely to be
responsible for a large fraction of the dust production rate in galaxies.
