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.
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