Once the finish is removed, the piece is rinsed off (the stripper blocks water from penetrating the wood). If the color needs to be changed, or stains removed like rust, a color remover can be applied and rinsed off. Sometimes, though, the color will not come off, and in that case either it should be left alone and finished like it is or a complementary color applied.
Right is after stripping and color removal (as much as possible - even using 12% straight bleach) and extensive sanding. You can see the areas of the curves still have a lot of color. Can you also see the 'tiger stripping' effect on the front horizontal piece in particular? This is because the pores are like soda straws and suck up a lot of color when applied. In this instance a stain was applied that was compatible with the color that wouldn't come out.