No, only those with a close stellar companion.
A Main Sequence star and a White Dwarf.
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Yes, when a star undergoes a nova, it expels material into space, which can eventually form a white dwarf. A white dwarf is the remnant core of a star that has exhausted its nuclear fuel and collapsed under gravity. Novae are different from supernovae, which are more energetic and can leave behind other remnants like neutron stars or black holes.
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Nova. "Exploding stars" were originally called "new stars", which in Latin is "nova stellarum".
A nova is a cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a white dwarf star. Nova are not to be confused with Type Ia supernovae which do explode [See Link]
A nova (as distinct from a supernova) is produced in a close binary system where one member is a white dwarf and the other a larger, less dense star. The white dwarf 'sucks' gas from the larger star which condenses into an accretion disc around the white star's equator. When this accretion disc reaches a critical mass it interacts with material on the white star and produces a huge thermonuclear explosion. This is what we see as a nova event. Novae are variable stars.
When a white dwarf star accretes hydrogen from a companion star, it can trigger a runaway nuclear fusion reaction that causes a sudden and bright increase in brightness called a nova. This explosion is not as powerful as a supernova, and the white dwarf usually survives to potentially experience multiple nova events.
White dwarf stage. Note that not all stars reach this stage. Some stars experience runaway criticality and go supernova. Also, white dwarf stars in binary systems can still go nova if they are acquiring hydrogen from their partner.
The explosion of a dwarf star is called a nova or a supernova, depending on the type of dwarf star and the circumstances of the explosion. Novas are less powerful explosions caused by a white dwarf siphoning material from a companion star, while supernovas are much more energetic explosions that can occur in white dwarfs or other types of stars.