  We show that some or all of the inventory of $r$-process nucleosynthesis can
be produced in interactions of primordial black holes (PBHs) with neutron stars
(NSs) if PBHs with masses ${10}^{-14}\,{\rm M}_\odot < {\rm M}_{\rm PBH} <
{10}^{-8}\,{\rm M}_\odot$ make up a few percent or more of the dark matter. A
PBH captured by a neutron star (NS) sinks to the center of the NS and consumes
it from the inside. When this occurs in a rotating millisecond-period NS, the
resulting spin-up ejects $\sim 0.1-0.5\,{\rm M}_{\odot}$ of relatively cold
neutron-rich material. This ejection process and the accompanying decompression
and decay of nuclear matter can produce electromagnetic transients, such as a
kilonova-type afterglow and fast radio bursts. These transients are not
accompanied by significant gravitational radiation or neutrinos, allowing such
events to be differentiated from compact object mergers occurring within the
distance sensitivity limits of gravitational wave observatories. The PBH-NS
destruction scenario is consistent with pulsar and NS statistics, the dark
matter content and spatial distributions in the Galaxy and Ultra Faint Dwarfs
(UFD), as well as with the $r$-process content and evolution histories in these
sites. Ejected matter is heated by beta decay, which leads to emission of
positrons in an amount consistent with the observed 511-keV line from the
Galactic Center.
