Sulindac in Preventing Melanoma in Healthy Participants Who Are at Increased Risk of Melanoma

Criteria: * Healthy participants at risk for developing melanoma and meeting the following criteria: must have \>= 4 large (\>= 5 mm and \< 15 mm) atypical nevi and have 1 benign nevus amenable to biopsies * No histologically confirmed melanoma on the baseline biopsy * No more than 1 prior cutaneous melanoma * One prior stage I, IIA, or IIB melanoma allowed provided patients have been off treatment \> 3 months * Modified dermoscopy score \< 4.8 * Karnofsky performance status 80-100% * ANC \>= 1,500/mm\^3 * No family history of melanoma involving \>= 2 first degree relatives * Platelets count \>= 100,000/mm\^3 * Total bilirubin =\< 2.0 mg/dL * AST/ALT =\< 2.0 times upper limit of normal * Creatinine =\< 1.5 mg/dL * Not pregnant or nursing * Fertile patients must use effective contraception * More than 6 months since prior and no concurrent tanning bed use or other methods to promote sun-tanning * Willing to minimize sunlight exposure by applying sunscreen/sunblock or wearing clothing to shield skin during outdoor activity during study participation * Willing or able to limit alcohol consumption to less than 3 servings a week during the study period * No frequent, chronic or moderate/severe gastrointestinal (GI) complaints * Upper GI problems requiring prescription or nonprescription medical remedies for symptoms of heartburn, dyspepsia, nausea, or abdominal pain \> once a week on average * History of peptic ulcer, occult or gross intestinal bleeding * No prior allergic reaction to aspirin (unless subsequent dosing with other NSAIDs has been well tolerated) * No history of allergic reaction to lidocaine or xylocaine * No history of allergic reaction (e.g., urticaria, asthma, or rhinitis) or gastric intolerance attributed to compounds of similar chemical or biological composition to sulindac * No invasive cancer or cancer treatment within the past 5 years, except nonmelanoma skin cancer * No immunosuppression by medication or disease, including any of the following: AIDS, oral prednisone, immunosuppressant/immunomodulator (i.e., cyclosporine, chemotherapeutic agent, or biologic therapy) * No uncontrolled intercurrent illness * No ongoing or active infection * No symptomatic congestive heart failure * No unstable angina pectoris * No cardiac arrhythmia * No psychiatric illness/social situations that would limit compliance with study requirements * At least 30 days since prior participation and no concurrent enrollment or planning to enroll in another clinical trial * No NSAIDs for more than 5 days per month within the past 3 months and no concurrent non-study NSAIDs, except low dose aspirin (81 mg/day) * Willing or able to refrain from herbal medicines, above-standard vitamins, or minerals during study * Standard daily multivitamin/mineral supplement (i.e., therapeutic doses of calcium and vitamin D for osteoporosis) allowed * No concurrent lithium, phenytoin, or sulfonamides * WBC \>= 3,000/mm\^3 * No history of bleeding or clotting disorder * At least 3 months since prior and no concurrent coumadin or other systemic anticoagulant other than aspirin