  More than 20 years ago, Glendenning, Kettner and Weber proposed the existence
of stable white dwarfs with a core of strange quark matter. More recently, by
studying radial modes, Alford, Harris and Sachdeva concluded instead that those
objects are unstable. We aim to clarify this issue. We investigate the
stability of these objects by looking at their radial oscillations while
incorporating boundary conditions at the quark-hadron interface, corresponding
to either a rapid or a slow conversion of hadrons into quarks. Our analysis
shows that objects of this type are stable if the star is not strongly
perturbed, and ordinary matter cannot transform into strange quark matter
because of the Coulomb barrier separating the two components. On the other
hand, ordinary matter can be transformed into strange quark matter if the star
undergoes a violent process, as in the preliminary stages of a type Ia
supernova, and this causes the system to become unstable and to collapse into a
strange quark star. In this way, accretion-induced collapse of strange dwarfs
can be facilitated, and km-sized objects with subsolar masses can be produced.
