Generally, the color of a toupee or any hairpiece for men should not lighten significantly after washing unless it is specifically designed to change color when exposed to water. If you have purchased a #2 dark brown toupee, it is unlikely to lighten noticeably after washing.
However, it’s important to note that certain factors can affect the appearance of the color after washing. For example, if the toupee is made from human hair and has been chemically treated or dyed, there might be some minimal fading over time with repeated washes. Additionally, exposure to sunlight or excessive heat styling can also cause slight changes in color over an extended period.