As our friend from Bellingham has indicated, bleach damage is not staining!
A stain is the result of added pigment. What chlorine bleach does is to chemically modify the native pigmentation by adding an oxygen molecule, thereby altering the manner in which the original colouring reacts to light, most commonly resulting in a broader spectrum of light to be reflected. Whilst it is often possible to alter the chemistry of the staining agent (sometimes with a bleaching agent), in most instances the bleaching action is irreversible. Hence the need to re-stain (re-dye) the fibres.