When a solar mass star is dying, how does it throw off a planetary nebula?

I was watching "How the Universe Works" on the Science Channel last night and they said something confusing. While describing the future transformation of the Sun into a white dwarf star, they mentioned that when the sun runs out of fuel the inward pull of gravity "wins" over the outward push of energy. Then they immediately described the shedding of solar material that would become a planetary nebula, leaving a white dwarf inside. My question is, if gravity "wins", then how did so much mass get shed by the star? It seems to me, without energy to support the star's current size, all the matter should contribute to the mass of the white dwarf? Thanks ahead of time for the clarity.