  The first Fast Radio Burst (FRB) to be precisely localized was associated
with a luminous persistent radio source (PRS). Recently, a second FRB/PRS
association was discovered for another repeating source of FRBs. However, it is
not clear what makes FRBs or PRS or how they are related. We compile FRB and
PRS properties to consider the population of FRB/PRS sources. We suggest a
practical definition for PRS as FRB associations with luminosity greater than
$10^{29}$ erg s$^{-1}$ Hz$^{-1}$ that is not attributed to star-formation
activity in the host galaxy. We model the probability distribution of the
fraction of FRBs with PRS for repeaters and non-repeaters, showing there is not
yet evidence for repeaters to be preferentially associated with PRS. We discuss
how FRB/PRS sources may be distinguished by the combination of active
repetition and an excess dispersion measure local to the FRB environment. We
use CHIME/FRB event statistics to bound the mean per-source repetition rate of
FRBs to be between 25 and 440 yr$^{-1}$. We use this to provide a bound on the
density of FRB-emitting sources in the local universe of between
$2.2\times10^2$ and $5.2\times10^4$ Gpc$^{-3}$ assuming a pulsar-like beam
width for FRB emission. This density implies that PRS may comprise as much as
1\% of compact, luminous radio sources detected in the local universe. The
cosmic density and phenomenology of PRS are similar to that of the
newly-discovered, off-nuclear "wandering" AGN. We argue that it is likely that
some PRS have already been detected and misidentified as AGN.
