High-Dose Aldesleukin and Ipilimumab in Treating Patients With Stage III-IV Melanoma That Cannot Be Removed By Surgery

Inclusion Criteria: * Willing and able to give written informed consent * Histologic or cytologic diagnosis of cutaneous melanoma that is considered unresectable (stage III) or metastatic (stage IV); ocular and mucosal melanoma is excluded * White blood cell (WBC) \>= 2000/uL * Absolute neutrophil count (ANC) \>= 1000/uL * Platelets \>= 75 x 10\^3/uL * Hemoglobin \>= 9 g/dL (\>= 80 g/L; may be transfused) * Creatinine =\< 2.0 x upper limit of normal (ULN) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN for patients without liver metastasis, =\< 5 times for patients with liver metastases * Bilirubin =\< 2.0 x ULN, (except patients with Gilbert's syndrome, who must have a total bilirubin less than 3.0 mg/dL) * No known active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C; testing is not required unless clinically suspected * Performance status (Eastern Cooperative Oncology Group \[ECOG\] 0-1) * Patients must have a life expectancy of greater than three months at the start of the trial * Patients must have a brain magnetic resonance imaging (MRI) that is free of active metastases; metastases that have been treated with radiation or surgical resection, are stable for at least 4 weeks and do not require steroids are eligible * Patients may have received treatment of completely resected early stage melanoma, comprising interferon, radiation treatment, or experimental vaccine therapy, and in the metastatic setting patient can have had treatment such as chemotherapy, immunotherapy (except prior treatment with ipilimumab and IL-2), and other experimental agent which was completed 4 weeks prior to enrollment * Normal cardiac stress test for patients over 50 years of age * Forced expiratory volume in 1 second (FEV1) \> 65% of prediction for those patients with extensive pulmonary metastases or chronic pulmonary disease history * Forced vital capacity (FVC) \> 65% of prediction for those patients with extensive pulmonary metastases or chronic pulmonary disease history * Women of childbearing potential (WOCBP) must be using an adequate method of contraception to avoid pregnancy throughout the study and for up to 26 weeks after the last dose of investigational product, in such a manner that the risk of pregnancy is minimized; in general, the decision for appropriate methods to prevent pregnancy should be determined by discussions between the investigator and the study subject; WOCBP include any female who has experienced menarche and who has not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or is not post-menopausal; post-menopause is defined as: * Amenorrhea \>= 12 consecutive months without another cause, or * For women with irregular menstrual periods and taking hormone replacement therapy (HRT), a documented serum follicle stimulating hormone (FSH) level \>= 35 mIU/mL * Women who are using oral contraceptives, other hormonal contraceptives (vaginal products, skin patches, or implanted or injectable products), or mechanical products such as an intrauterine device or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy, or are practicing abstinence or where their partner is sterile (eg, vasectomy) should be considered to be of childbearing potential * WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 72 hours before the start of ipilimumab * Men of fathering potential must be using an adequate method of contraception to avoid conception throughout the study (and for up to 26 weeks after the last dose of investigational product) in such a manner that the risk of pregnancy is minimized Exclusion Criteria: * Any other malignancy form which the patient has been disease-free for less than 5 years, with the exception of adequately treated and cured basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix * Patients with primary ocular or mucosal melanoma are excluded * Patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic disease (eg, rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[eg, Wegener's granulomatosis\]); motor neuropathy considered of autoimmune origin (e.g. Guillain-Barre syndrome and Myasthenia Gravis) * Any underlying medical or psychiatric condition, which in the opinion of the investigator will make the administration of ipilimumab hazardous or obscure the interpretation of adverse events (AEs), such as a condition associated with frequent diarrhea * Patients with underlying heart conditions who are deemed ineligible for surgery by cardiology consult; patients with reversible ischemic changes on cardiac stress test * Any non-oncology vaccine therapy used for prevention of infectious diseases (for up to 1 month before or after any dose of ipilimumab) * A history of prior treatment with IL-2, ipilimumab or prior cytotoxic T-lymphocyte antigen 4 (CTLA4) inhibitor or agonist * Concomitant therapy with any of the following: interferon, or other non-study immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive agents; other investigation therapies; or chronic use of systemic corticosteroids * Women of childbearing potential (WOCBP), who: * Are unwilling or unable to use an acceptable method of contraception to avoid pregnancy for their entire study period and for at least 8 weeks after cessation of study drug, or * Have a positive pregnancy test at baseline, or * Are pregnant or breastfeeding * Prisoners or subjects who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (eg, infectious) illness