Papaya soap does not contain skin-bleaching agents and, as such, is not designed for skin whitening. However, it does contain the protein-cleaving enzyme papain, according to Wikipedia. Papain removes dead skin cells, which may slightly lighten the skin.
Papain has not been approved by the Food and Drug Administration and may be unsafe if used incorrectly. Products containing papain, such as papaya soap, are typically used to remove dead or contaminated tissue from lesions such as diabetic ulcers and traumatic infected wounds. Using products containing papain for skin-whitening purposes is not recommended, as no clinical trials have been conducted on its effectiveness or safety when used in such a way, notes the FDA.