Everybody knows chlorine ($\ce{Cl2}$) is a bleaching agent acting on oxidation. However, what majority of us do not know is sulfur dioxide ($\ce{SO2}$) is also a bleaching agent, which in contrast to $\ce{Cl2}$, acting on reduction (though we know about other reducing sulfur agents such as sodium dithionite and thiosulfate). The well-known Encyclopaedia Britannica simply explain it as:
Wood and animal fibres are bleached by acidic reducing agents such as sulfur dioxide. In the pulp and paper industry chlorine dioxide, hydrogen peroxide, sodium peroxide, sulfur dioxide, sodium bisulfite, and sodium hydrosulfite are commonly used.
Bleaching agents, regardless of oxidizing or reducing, are formulations that whiten or lighten a substrate by solubilizing color-producing substances or by altering their light-absorbing properties. The decolorizing reaction generally involves the removal of chromophoric sites in which electron delocalization over conjugated double bonds has made the substrate capable of absorbing visible light. The bleaching agent will typically react by irreversibly cleaving or adding across these double bonds (Ref.1). If the bleaching is done by oxidation, the conjugation is broken irreversibly (e.g., converting double bonds to diols), and permanently because there is no reducing agents in air. Even sunlight helps the oxidation, which is the chief bleaching method of textiles (a process known as crofting) used before the discovery of the element chlorine in 1774.
If the bleaching is done by reduction, it is a different story. According to Ref.1:
A few bleaching compounds act by chemical reduction; these include sulfur dioxide ($\ce{SO2}$), sulfurous acid ($\ce{H2SO3}$), hydrogensulfite ($\ce{HSO3−}$), sulfite ($\ce{SO3^2−}$), and dithionite ($\ce{S2O4^2−}$), as well as sodium tetrahydroborate (borohydride) ($\ce{NaBH4}$). Their application is primarily in pulp and textile manufacturing, where the bleaching action is thought to occur by reduction of a chromophoric carbonyl group. Other applications include the bleaching of glues, gelatin, soap, and food products.
These reduced chromophores would be regenerated slowly by the atmospheric oxygen (recall oxidation and reduction of indigo dye as Buttonwood explained in comment section). Thus, the bleaching by reduction is not permanent in most cases.
Late addition: After I submitted my answer, I have seen the conversation between OP and other commenters. I felt OP have not so correct idea of bleaching. Bleaching action is not removing oxygen or obtaining nascent oxygen. It is about the breaking the chromophore responsible for the color. I think I have explained the principle quite clearly in my answer above. Basically, regardless of bleaching of oxidation or reduction, it breaks the conjugation of the chromophore, which is responsible for the color (you want to get rid of). If it is done by oxidation, the color can't get back because no reducing agents in our atmosphere. Yet, if the bleaching is done reduction, the relevant chromophore would able to get its conjugation back with help of atmospheric $\ce{O2}$ (or $\ce{O^.}$).
Also, I like to point to a nice demonstration of bleaching by $\ce{SO2}$ here.
References:
- Marianna A. Busch, Kenneth W. Busch, in Encyclopedia of Analytical Science (Third Edition); Alan Townshend, Editor-in-Chief; Elsevier Science Ltd: Amsterdam, Netherlands, 2019 (ISBN: 9780081019832).
