Now this topic sounds nuts but what you read further might convince you to accept the possibility of the existence of a star within a star.
The Thorne Zytkow object is type of star speculated on the basis of incomplete evidence which proposes the possibility of a neutron star existing at the core of a red giant. This idea was given by Kip Thorne and Anna Zytkow in 1977.
Formation of the Star
This type of star might form in a binary star system wherein one star undergoes a supernova to form a neutron star. The companion star, if a main sequence star( like our sun) will engulf the neutron star when its outer layers expand to form a red giant or if the system already has a red giant, the supernova explosion of the first star might cause it to cross paths with the red giant companion. After the neutron star enters the red giant, drag from the layers of the red giant will cause the neutron star to slow down and collide with its core. If the combined mass of the core and the neutron does not exceeds a limit known as the tolmann-oppenheimer-volkoff (upper mass limit of a neutron star to remain a neutron star), the whole thing will become a black hole.