In the case of two white dwarfs, the two stars spiral closer and closer, giving off gravitational radiation, until they collide. In the case of one white dwarf and a regular star, as the stars evolve and begin to spiral closer to each other, they reach a point where mass transfer begins. This mass transfer stabilizes the orbit so that the two stars no longer move closer to each other and will not collide, as in the case of the two white dwarfs.
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