  (Abridged) Until recently the information inferred from gamma-ray burst
follow-up observations was mostly limited to optically bright afterglows,
biasing all demographic studies against sight-lines that contain large amounts
of dust. Here, we present GRB afterglow and host observations for a sample of
bursts that are exemplary of previously missed ones because of high visual
extinction along the sight-line. This facilitates an investigation of the
properties, geometry and location of the absorbing dust of these
poorly-explored host galaxies, and a comparison to hosts from
optically-selected samples. The hosts of the dustiest afterglows are diverse in
their properties, but on average redder, more luminous and massive than the
hosts of optically-bright events. We hence probe a different galaxy population,
suggesting that previous host samples miss most of the massive,
chemically-evolved and metal-rich members. This also indicates that the dust
along the sight-line is often related to host properties, and thus probably
located in the diffuse ISM or interstellar clouds and not in the immediate GRB
environment. Some of the hosts in our sample, are blue, young or of small
stellar mass illustrating that even apparently non-extinguished galaxies
possess very dusty sight-lines due to a patchy dust distribution. The presented
observations establish a population of luminous, massive and correspondingly
chemically-evolved GRB hosts. This suggests that GRBs trace the global
star-formation rate better than studies based on optically-selected host
samples indicate, and the previously-claimed deficiency of high-mass host
galaxies was at least partially a selection effect.
