In this study, asteroid families (AFs) were researched beyond the limits of observational possibilities. The first step of this work was the selection of some AFs from a data set containing more than 400000 numbered asteroids. The hierarchical clustering method (HCM) was then applied to the selection, and a full set of the N asteroid family members (AFMs) of the considered family was sorted according to mass. Next, the assumed formula for asteroid mass distribution dn ​= ​Bm-γ dm was fitted to several intervals (n1, n2) where 2 ​< ​n1 ​< ​n2 ​< ​N. As a result, it was found that both parameters (B, γ) decreased when the interval (n1, n2) shifted to larger numbers. This trend held for all of the AFs considered. Based on these findings, we extrapolated the mass distribution of each AF up to the indefinitely small masses. This extrapolation allowed us to calculate the masses of the tails composed of small asteroids, most of which were non-observable. The ‘tails’ of the AFs contained asteroids with an absolute magnitude H higher than the H′ that was individually fitted for each family; H′ ranged between 15.4 (Eunomia family) and 17.2 (Massalia family). The mass ratio F = (Calculated mass of the tail)/(Observed mass of the tail) for eight families was calculated.