Recently, constraints on bosonic asymmetric dark matter have been imposed based on the existence of old neutron stars, excluding dark matter masses in the range from ∼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 quickly 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.