Hawking (1988: 83-4):
Chandrasekhar worked out how big a star could be and still support itself against its own gravity after it had used up all its fuel. The idea was this: when the star becomes small, the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities. This makes them move away from each other and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life gravity was balanced by the heat.
Chandrasekhar realised, however, that there is a limit to the repulsion that the exclusion principle can provide. The theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light. This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar limit.)
From the perspective of Systemic Functional Linguistic Theory, according to General Relativity, the star "becoming small" under gravity is actually the contraction of the space occupied by the star, and it is this that brings the matter particles closer together.
On the other hand, the expansion of the star due to the repulsion of particles, as described by the Pauli exclusion principle, is the expansion of the volume of the matter-energy occupying the space, not the expansion of space itself.
That is, the balance that is achieved is between the gravitational contraction of space intervals and the expansion of the volume of the matter-energy (the star itself).
When the density of a star reduces the amount of particle repulsion, the volume of the star no longer counterbalances the gravitational contraction of the space it occupies, and the star is no longer 'able to support itself against its own gravity'.