Final answer:
Degeneracy pressure fails to stop gravitational contraction in the core of a high-mass star, which can lead to the formation of neutron stars or black holes, unlike in brown dwarfs and white dwarfs where degeneracy pressure stabilizes the object against further collapse.
Step-by-step explanation:
In the case of objects where degeneracy pressure fails to stop gravitational contraction, the core of a high-mass star is the one that cannot be supported by degeneracy pressure alone. A brown dwarf and a white dwarf both are supported by degeneracy pressure, preventing further collapse. A brown dwarf is stabilized by the degeneracy pressure of electrons, as is a white dwarf. However, the core of a high-mass star collapses further because the electron degeneracy pressure is overcome by the enormous gravity when the core's mass exceeds the Chandrasekhar limit, leading to the formation of neutron stars or black holes after a supernova event.