Which rare skin cancer commonly develops in individuals with weakened immune systems?

Kaposi's sarcoma is a rare form of skin cancer that frequently occurs in individuals with weakened immune systems, particularly those with HIV/AIDS or other conditions that compromise immune function. This cancer is characterized by the growth of tumors in the form of purple, bluish-red, or brown patches on the skin, which are caused by the abnormal proliferation of blood vessels. The association between Kaposi's sarcoma and immune suppression highlights its relevance in patients whose immune responses are not adequately functioning, making them more susceptible to this condition.

In this context, the other types of skin cancer mentioned, while significant, are generally more commonly found in the general population and are not predominantly linked to immune system status. Melanoma arises from pigment-producing cells and can affect anyone, but it doesn’t have the same strong association with immune suppression. Basal cell carcinoma and squamous cell carcinoma are the most common forms of non-melanoma skin cancer and are primarily linked to UV exposure rather than immune status. Thus, the distinctive connection of Kaposi's sarcoma to compromised immune conditions makes it the correct answer.