It has been argued that the low-mass primordial stars (m Pop III ≤ 0.8 M ⊙) are likely to enter the main sequence and hence may possibly be found in present-day galaxies. However, due to limitations in existing numerical capabilities, current three-dimensional (3D) simulations of disk fragmentation are only capable of following a few thousand years of evolution after the formation of the first protostar. In this work, we use a modified version of the Gadget-2 smoothed particle hydrodynamics code to present the results of the nonlinear collapse of the gas clouds associated with various degrees of initial solid body rotation (parameterized by β) using a piecewise polytropic equation of state. The 3D simulations are followed until the epoch that occurs when 50M ⊙ of mass has been accreted in protostellar objects, which is adequate enough to investigate the dynamics of the protostars with the surrounding gaseous medium and to determine the mass function, accretion rate, and possibility of the survival of these protostellar objects to the present epoch. We found that evolving protostars that stay within slow-rotating parent clouds can become massive enough to survive, due to accretion in the absence of radiative feedback, whereas 10%–12% of those formed within fast-rotating clouds (β ≥ 0.1) could possibly be ejected from the gravitational bound cluster as low-mass stars.