Can a white dwarf end up inside a red giant?

What you're describing is essentially an Asymptotic Giant Branch (AGB) star right before it produces a planetary nebula. Stars at the end/tip of the AGB have degenerate cores (i.e. they're already white dwarfs inside). When they enter the planetar... read more

This is because they have solid inner cores and that would cause some complications. However, materials once in a white dwarf can eventually end up in a red giant over the course of millions of years. Maybe somebody with some more knowledge can prove me wrong, though. read more

Smaller stars, such as red dwarfs, don't make it to the red giant state. They simply burn through all of the hydrogen within the star, leaving behind the shell that is a white dwarf. However, red dwarfs take trillions of years to consume their fuel, far longer than the 13.8-billion-year-old age of the universe, so no red dwarfs have yet become white dwarfs. read more