  Interstellar small bodies are unique probes into the histories of
exoplanetary systems. One hypothesized class of interlopers are "Jurads,"
exo-comets released into the Milky Way during the post-main sequence as the
thermally-pulsing asymptotic giant branch (AGB) host stars lose mass. In this
study, we assess the prospects for the Legacy Survey of Space and Time (LSST)
to detect a Jurad and examine whether such an interloper would be
observationally distinguishable from exo-comets ejected during the (pre-)main
sequence. Using analytic and numerical methods, we estimate the fraction of
exo-Oort Cloud objects that are released from 1-8 solar mass stars during
post-main sequence evolution. We quantify the extent to which small bodies are
altered by the increased luminosity and stellar outflows during the AGB,
finding that some Jurads may lack hypervolatiles and that stellar winds could
deposit dust that covers the entire exo-comet surface. Next, we construct
models of the interstellar small body reservoir for various size-frequency
distribution slopes, characteristic sizes, and the total mass sequestered in
the minor planets of exo-Oort Clouds. Even with the LSST's increased search
volume compared to contemporary surveys, we find that detecting a Jurad is
unlikely but not infeasible given the current understanding of (exo)planet
formation.
