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degenerate dwarf (commonly called white dwarf), neutron star and quark star. The first two have been conclusively observed to exist in nature, while the latter may be represented in RX J1856.5-3754 and 3C58, though observations are inconclusive.
In general in a star the gravitational pull of matter tends to squeeze the star to smaller size, but most stars are in a state of static equilibrium (where gravity is exactly counterbalanced by other forces) and they remain a constant size.
In general, in main sequence stars (our Sun is a main sequence star), gravitational pressure is counterbalanced by the thermal motion of the star's atoms.
A star which is gravitationally compacted to a greater density than that of a degenerate star is a stellar mass black hole
If the gravitational pressure is strong enough to overcome thermal motion, as for example when fusion slows or ceases from lack of fuel, the next potential equilibrium state is due to electron degeneracy pressure.
A star like this is composed of electron degenerate matter, supported against gravity only by the resistance of electrons to being squeezed into the same energy state around the nucleus (as described by the Pauli exclusion principle).
Such a star is called a degenerate dwarf, or more commonly a white dwarf. A cold white dwarf is known as the theoretical black dwarf. They were observed for the first time in the 19th century, but the extremely high densities and pressures were not explained until 1932.
If the gravitational pressure is still larger, electrons are forced into the nucleii where they merge with protons, creating baryon degenerate matter. The entire star becomes a homogenous lump of neutrons, and is called a neutron star.
The existence of neutron stars was predicted on theoretical grounds in 1933 as a possible state of a large number of neutrons, amounting to about the mass of the Sun. In 1963 neutron stars were for the first time observed as radio pulsar, later also as stellar x-ray source.
In theory, if gravitational pressure is even stronger, the matter in the star may be reduced to a soup of quarks, called a quark star or less generally a strange star. There have not yet been any confirmed observations of quark stars. The interior of the star would be akin to a giant nucleon.
Hypothetically, if gravitational pressure were stronger, stellar matter would be reduced to quark constituents, preons or sub-quarks. The preon star would then be a giant quark. The basis of sub-quarks in theory is not generally accepted. Preons do not exist as part of the Standard Model of quantum physics.