In our earlier studyDutta (2016a), it has been shown that a number of primordial protostars (the ‘first stars’ in the Universe, also known as Population III or Pop III stars) are being ejected from the cluster of their origin with the velocity exceeding their escape velocity. Hence there is possibility that some of these protostars can enter main sequence and survive till present epoch, even in Milky Way. We ask the question if the protostars can avoid core collapse, and stop accreting before being ejected from the cluster, with the final mass of stars as 0.8 Mȯ.