  We identify new astrophysical signatures of dark matter that implodes neutron
stars (NSs), which could decisively test whether NS-imploding dark matter is
responsible for missing pulsars in the Milky Way galactic center, the source of
some $r$-process elements, and the origin of fast-radio bursts. First,
NS-imploding dark matter forms $\sim 10^{-10}$ solar mass or smaller black
holes inside neutron stars, which proceed to convert neutron stars into
$\sim$1.5 solar mass BHs. This decreases the number of neutron star mergers
seen by LIGO/Virgo (LV) and associated merger kilonovae seen by telescopes like
DES, BlackGEM, and ZTF, and instead, producing a population of "black mergers"
containing $\sim$1.5 solar mass black holes. Second, dark matter-induced
neutron star implosions may create a new kind of kilonovae that lacks a
detectable, accompanying gravitational signal, which we call "quiet kilonovae."
Using DES data and the Milky Way's r-process abundance, we constrain quiet
kilonovae. Third, the spatial distribution of neutron star merger kilonovae and
quiet kilonovae in galaxies can be used to detect dark matter. NS-imploding
dark matter destroys most neutron stars at the centers of disc galaxies, so
that neutron star merger kilonovae would appear mostly in a donut at large
radii. We find that as few as ten neutron star merger kilonova events, located
to $\sim$1 kpc precision could validate or exclude dark matter-induced neutron
star implosions at $2 \sigma$ confidence, exploring dark matter-nucleon
cross-sections 4-10 orders of magnitude below current direct detection
experimental limits. Similarly, NS-imploding dark matter as the source of fast
radio bursts can be tested at $2 \sigma$ confidence once 20 bursts are located
in host galaxies by radio arrays like CHIME and HIRAX.
