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