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A challenging problem facing AC-Quasi-Steady-State (AC-QSS) cascading failure models of power system is the divergence issue primarily stemming from voltage collapse phenomena. In reality, there are undervoltage load shedding (UVLS) relays, which aim to prevent such a collapse by shedding a pre-specified fraction of load at buses where the corresponding voltages fall below a threshold. However, capturing the UVLS action in QSS models is very difficult, because most of the time the model cannot generate an equilibrium below the voltage threshold due to divergence. To address this problem, current models have applied different variants of uniform load shedding (ULS) till convergence is achieved, which differ from the ground truth. In order to solve this, we propose a methodology that leverages the post-ULS load flow as a starting point when divergence occurs. In this condition, a sensitivity index coupled with the voltage magnitudes of buses is used to recognize the buses that are most prone to voltage collapse. The UVLS scheme is then applied to these buses. To verify the accuracy of the results, we also present a suitable dynamic cascade model with appropriate limits and protection details that can selectively capture UVLS action, thereby revealing the proximate ground truth. Predictions of the proposed model are validated against those of the dynamic model for representative cases in IEEE 118-bus system. In addition, results of the proposed model are contrasted with two ULS schemes on the 2, 383-bus Polish system.