  Fast radio bursts (FRBs) are an emerging class of short and bright radio
transients whose sources remain enigmatic. Within the galactic center, the
non-detection of pulsars within the inner $\sim \!10\,{\rm pc}$ has created a
missing pulsar problem that has intensified with time. With all reserve, we
advance the notion that the two problems could be linked by a common solution:
the collapse of neutron stars (NS) due to capture and sedimentation of dark
matter (DM) within their cores. Bramante \& Linden (2014), Phys.\ Rev.\
Lett.~19, 191301 showed that certain DM properties allow for rapid NS collapse
within the high DM density environments near galactic centers while permitting
NS survival elsewhere. Each DM-induced collapse could generate an FRB as the NS
magnetosphere is suddenly expelled. This scenario could explain several
features of FRBs: their short time scales, large energies, locally produced
scattering tails, and high event rates. We predict that FRBs are localized to
galactic centers, and that our own galactic center harbors a large population
of NS-mass ($M\sim1.4 M_\odot$) black holes. The DM-induced collapse scenario
is intrinsically unlikely because it can only occur in a small region of
allowable DM parameter space. However, if observed to occur, it would place
tight constraints on DM properties.
