Novae have never been observed to occur in Supernova remnant white dwarfs.
The building that remains after a supernova explosion is called a supernova remnant (SNR). The supernova remnant, which is surrounded by an expanding shock wave, is made up of material that was expelled from the explosion and is expanding, as well as interstellar debris that the shock wave has swept up along the way.
One of two processes can cause a star to go supernova: either by exhausting all of its fuel, ceasing to produce fusion energy in its core, and collapsing in on itself to form a neutron star or a black hole; or by accreting material from a companion star until it reaches a critical mass and erupts in a thermonuclear explosion.
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