As said in the article on stars, there is a constant equilibrium between gravity and the heat and energy produced by a star during its life. Yet, during a star's death stages, the heat and energy produced by the fusion decreases along with the hydrogen fuel, but gravity still remains the same. Due to this, a star begins to contract. As it does this, the particles within it begin to come closer and closer to each other. As they came closer and closer, the exclusion principle would become more evident. In other words, the velocities of the particles within the star would rise so much during the contraction phase, that the energy and heat they created would once again create an equilibrium with gravity.
What Chandrasekhar said was that there was a certain limit to the size of the star before even the exclusion principle would not cancel out gravity. In other words, the repelling forces of the particles, following the exclusion principle, would not be enough to withstand the star's gravity. Since the particles could not reach velocities equaling that of light, gravity would take over. So Chandrasekhar calculated that a star about 1.5 times the mass of our sun, would not be able to support itself under its own gravity. This mean that stars under this limit, would contract and stop at some point, creating a star known as a white dwarf. Another physicist, Lev Landau said that a star with a mass of about 1-2 times that of the sun could also become a neutron star. This could occur because even though the exclusion principle would break down for electrons, the one for protons and neutrons would come into effect. Yet stars over this limit would have a gravitational force that would overcome the exclusion principles for electrons, protons and neutrons. In this case, their fate would be a supernova, which would result in the star shrinking to zero size. In other words, a singularity would be created, or an infinitely small point of infinite density: a black hole.