Cystine is an amino acid containing a sulfur atom and is an oxidized version of cysteine. It is abundant in keratin, which is the main protein of human hair. It is also one of our body's natural antioxidants due to the presence of the sulfur atom, although this is the reason for its characteristic smell and relatively low stability.
It is added to skincare products as an antioxidant ingredient, but also has some mild anti-pigment properties and can allegedly also help in anti-aging preparations. However, due to its lower stability and mildly unpleasant smell, it is not used very often.
Hair-waving agents are one of the only cosmetic products where you'll find lysine in large amounts.
Science
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Oshimura, E., & Sakamoto, K. (2017). Amino Acids, Peptides, and Proteins. Cosmetic Science and Technology, 285–303.