  Several recent studies have indicated that artificial subhalo disruption (the
spontaneous, non-physical disintegration of a subhalo) remains prevalent in
state-of-the-art dark matter-only cosmological simulations. In order to
quantify the impact of disruption on the inferred subhalo demographics, we
augment the semi-analytical SatGen dynamical subhalo evolution model with an
improved treatment of tidal stripping that is calibrated using the DASH
database of idealized high-resolution simulations of subhalo evolution, which
are free from artificial disruption. We also develop a model of artificial
disruption that reproduces the statistical properties of disruption in the
Bolshoi simulation. Using this framework, we predict subhalo mass functions
(SHMFs), number density profiles, and substructure mass fractions and study how
these quantities are impacted by artificial disruption and mass resolution
limits. We find that artificial disruption affects these quantities at the
$10-20\%$ level, ameliorating previous concerns that it may suppress the SHMF
by as much as a factor of two. We demonstrate that semi-analytical substructure
modeling must include orbit integration in order to properly account for
splashback haloes, which make up roughly half of the subhalo population. We
show that the resolution limit of $N$-body simulations, rather than artificial
disruption, is the primary cause of the radial bias in subhalo number density
found in dark matter-only simulations. Hence, we conclude that the mass
resolution remains the primary limitation of using such simulations to study
subhaloes. Our model provides a fast, flexible, and accurate alternative to
studying substructure statistics in the absence of both numerical resolution
limits and artificial disruption.
