  Recently, constraints on bosonic asymmetric dark matter have been imposed
based on the existence of old neutron stars excluding the dark matter masses in
the range from $\sim 2$ keV up to several GeV. The constraints are based on the
star destruction scenario where the dark matter particles captured by the star
collapse forming a black hole that eventually consumes the host star. In
addition, there were claims in the literature that similar constraints can be
obtained for dark matter masses heavier than a few TeV. Here we argue that it
is not possible to extend to these constraints. We show that in the case of
heavy dark matter, instead of forming a single large black hole that consumes
the star, the collapsing dark matter particles form a series of small black
holes that evaporate fast without leading to the destruction of the star. Thus,
no constraints arise for bosonic asymmetric dark matter particles with masses
of a few TeV or higher.
