Any colored fabric, including fake fur, can be bleached (or discolored) with chlorine bleach. The actual bleaching chemical in most chlorine based bleaches is sodium hypochlorite. This is a very powerful oxidizing agent that dissolves in water. The way that chlorine beach works is that most dyes and colorants contain molecules with complex systems of chemical double bonds. These networks of double bonds give the compounds unique and interesting light absorbing properties, thus giving rise to the vibrant colors. The sodium hypochlorite oxidizes and disrupts these double bonds by either converting them to single bonds or breaking up the bonds entirely. Either way, the dyes lose their light aborbance properties and hence their colors. So any dye colored fabric, including fake fur, can be bleached to lose its color.