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Globular clusters (GCs) are often used to estimate the dark matter content of galaxies, especially dwarfs, where other kinematic tracers are lacking. These estimates typically assume spherical symmetry and dynamical equilibrium, assumptions that may not hold for the sparse GC population of dwarfs in galaxy clusters. We use a catalog of GCs tagged onto the Illustris simulation to study the accuracy of GC-based mass estimates. We focus on galaxies in the stellar mass range 10$^{8} - 10^{11.8}$ M$_{\odot}$ identified in $9$ simulated Virgo-like clusters. Our results indicate that mass estimates are, on average, quite accurate in systems with GC numbers $N_{\rm GC} \geq 10$ and where the uncertainty of individual GC line-of-sight velocities is smaller than the inferred velocity dispersion, $σ_{\rm GC}$. In cases where $N_{\rm GC} \leq 10$, however, biases may result depending on how $σ_{\rm GC}$ is computed. We provide calibrations that may help alleviate these biases in methods widely used in the literature. As an application, we find a number of dwarfs with $M_{*} \sim 10^{8.5}\, M_{\odot}$ (comparable to the ultradiffuse galaxy DF2, notable for the low $σ_{GC}$ of its $10$ GCs) with $σ_{\rm GC} \sim 7$ - $15\; \rm km \rm s^{-1}$. These DF2 analogs correspond to relatively massive systems at their infall time ($M_{200} \sim 1$ - $3 \times 10^{11}$ $M_{\odot}$) which have retained only $3$-$17$ GCs and have been stripped of more than 95$\%$ of their dark matter. Our results suggest that extreme tidal mass loss in otherwise normal dwarf galaxies may be a possible formation channel for ultradiffuse objects like DF2.