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The vector interaction enhanced Bag model (vBag) for dense quark matter extends the commonly used thermodynamic Bag model (tdBag) by incorporating effects of dynamical chiral symmetry breaking (D χ SB) and vector repulsion. Motivated by the suggestion that the stability of strange matter is in tension with chiral symmetry breaking (D χ SB) we examine the parameter space for its stability in the vBag model in this work. Assuming the chiral transition occurs at sufficiently low density, we determine the stability region of strange matter as a function of the effective Bag constant and the vector coupling. As an astrophysical application, we construct contours of maximum mass M max and radius at maximum mass R max in this region of parameter space. We also study the stability of strange stars in the vBag model with maximum mass in the 2 M ⊙ range by computing the spectrum of radial oscillations, and comparing to results from the tdBag model, find some notable differences.