  Passive early-type galaxies (ETGs) provide an ideal laboratory for studying
the interplay between dust formation around evolved stars and its subsequent
destruction in a hot gas. Using Spitzer-IRS and Herschel data we compare the
dust production rate in the envelopes of evolved AGB stars with a constraint on
the total dust mass. Early-type galaxies which appear to be truly passively
evolving are not detected by Herschel. We thus derive a distance independent
upper limit to the dust grain survival time in the hostile environment of ETGs
of < 46 +/- 25 Myr for amorphous silicate grains. This implies that ETGs which
are detected at far-infrared wavelengths have acquired a cool dusty medium via
interaction. Given likely time-scales for ram-pressure stripping, this also
implies that only galaxies with dust in a cool (atomic) medium can release dust
into the intra-cluster medium.
