  The global visibility of a singularity as an end state of the gravitational
collapse of a spherically symmetric pressureless cloud is investigated. We show
the existence of a non-zero measured set of parameters: the total mass and the
initial mean density of the collapsing cloud, giving rise to a physically
strong globally visible singularity as the end state for a fixed velocity
function. The existence of such a set indicates that such singularity is stable
under small perturbation in the initial data causing its existence. This is
true for marginally as well as non-marginally bound cases. The possibility of
the presence of such suitable parameters in the astrophysical setup is then
studied: $1)$ The singularities' requirements at the center of the M87 galaxy
and at the center of our galaxy (SgrA*) to be globally visible are discussed in
terms of the initial size of the collapsing cloud forming them, presuming that
such singularities are formed due to gravitational collapse. $2)$ The
requirement for the primordial singularities formed due to a collapsing
configuration after getting detached from the background universe, at the time
of matter-dominated era just after the time of matter-radiation equality, to be
globally visible, is discussed. $3)$ The scenario of the collapse of a neutron
star after reaching a critical mass, which is achieved by accreting the
supernova ejecta expelled by its binary companion core progenitor, is
considered. The primary aim of this paper is to show that globally visible
singularities can form in astrophysical setups under appropriate circumstances.
