  By means of 3-D hydrodynamical simulations, here we evaluate the impact that
supernova explosions occurring within wind-driven bubbles have on the survival
or destruction of dust grains. We consider both, the dust generated within the
ejecta and the dust initially present in the ambient gas and later locked-up in
the surrounding wind-driven shell. The collision of the supernova blast wave
with the wind-driven shell leads to a transmitted shock that moves into the
shell and a reflected shock into the ejecta. The transmitted shock is capable
of destroying large amounts of the dust locked in the shell, but only if the
mass of the wind-driven shell is small, less than a few tens the ejected mass.
Conversely, massive wind-driven shells, with several times the ejected mass,
lead upon the interaction to strong radiative cooling, which inhibits the
Sedov-Taylor phase and weakens the transmitted shock, making it unable to
traverse the wind-driven shell. In such a case, the destruction/disruption of
the ambient dust is largely inhibited. On the other hand, the SNRs grow rapidly
in the very tenuous region excavated by the stellar winds, and thus a large
fraction of the dust generated within the ejecta is not efficiently destroyed
by the supernova reverse shock, nor by the reflected shock. Our calculations
favor a scenario in which core-collapse supernovae within sufficiently massive
wind-driven shells supply more dust to the ISM than what they are able to
destroy.
