Zodiacal dust bands are an observational signature of the dust released in the family-forming, catastrophic disruption of asteroids. Previous detailed dynamical modeling of the structure of a young, still forming, zodiacal dust band has shown that partial dust bands retain significant information about both the size-frequency distribution and cross-sectional area of dust released by the disruption of their parent asteroids (Espy-Kehoe et al., 2016). Applying the observational constraints provided by partial dust bands to our models of the dynamical evolution of the dust composing the bands allows us to extract key information regarding the properties of the regolith on the surface of the parent asteroid before its collisional disruption, including the depth of the regolith and the size distribution of the particles present. In particular, using the constraints provided by modeling the faint partial dust band at an ecliptic latitude of 17 degrees, we investigate the relationship between regolith depth and the size distribution of the particles present; place these values in the wider context of values determined for other asteroid surfaces; and place constraints on the temporal variation of the magnitude of the zodiacal cloud following a recent asteroid disruption. The results indicates a scaling relationship between regolith depth and the diameter of the asteroid parent body that may be a useful discriminant of potential regolith production mechanisms and which imply that the dust released in the catastrophic disruption of an asteroid is dominated by the ejection of its surface regolith particles. Our modeling indicates that disrupting a single body with diameter ~100 km will be enough to regenerate the entire zodiacal cloud, while a body with diameter ~250 km could theoretically generate a debris disk with an order of magnitude greater optical depth. The breakup of smaller asteroids with diameters ~10 km will likely produce more moderate, but still significant, changes in the dust environment of the inner solar system. As collisional disruptions of asteroids in this size range occur more frequently, it is important that we develop a better understanding of the injection of asteroidal material as a result of these type of events in order to determine the recent temporal evolution of the zodiacal cloud and improve engineering models of the impact threat posed by the natural meteoroid environment to the utilization and exploration of space.