Ipilimumab or High-Dose Interferon Alfa-2b in Treating Patients With High-Risk Stage III-IV Melanoma That Has Been Removed by Surgery

Inclusion Criteria: * All patients must have disease-free status documented by a complete physical examination and imaging studies within 4 weeks prior to randomization; imaging studies must include a total body positron emission tomography (PET)-computed tomography (CT) scan (with or without brain) and brain magnetic resonance imaging (MRI) or CT (if MRI is contraindicated); if PET-CT cannot be done, CT of neck, chest, abdomen, and pelvis should be done * If for some reason a CT cannot be done, an MRI may be done instead; any other imaging studies if performed (eg, bone scan) must show no evidence of disease * Patients must have primary cutaneous melanoma that belong to one of the following American Joint Commission on Cancer (AJCC) stages (2009 AJCC Melanoma Staging System): * Stage IIIB * T1-4b N1a M0 * T1-4b N2a M0 * T1-4b N1b M0 * T1-4b N2b M0 * T1-4b N2c M0 * Stage IIIC * T1-4b N1b M0 * T1-4b N2b M0 * T1-4b N2c M0 * Any T N3 M0 * Stage IV * M1a * M1b * NOTE: patients with stage IV melanoma must have normal lactate dehydrogenase (LDH) and either distant skin, subcutaneous, lymph node, or lung metastases, but no other visceral metastases in order to be eligible; for patients with resected stage IV melanoma, LDH within the institutional upper limit of normal (ULN) must be documented within 4 weeks prior to randomization * Patients with disease recurrence after adequate surgical excision of the original primary cutaneous/unknown primary melanoma are allowed even if they don't fit the strict staging criteria, but only as follows: * Recurrence in a regional lymph node basin after a prior complete lymph node dissection; relapsed disease must be completely surgically resected with free margins * Recurrence in the form of in-transit or satellite metastases or distant skin/subcutaneous, nodal, or lung metastases that are completely surgically resected with free margins * Recurrence in a regional lymph node basin; relapsed disease must be completely surgically resected with free margins * Patients with unknown primary melanoma (Tx) who present with cutaneous, subcutaneous, nodal and/or lung metastases that are completely surgically resected with free margins are allowed; these patients are allowed even if they don't fit the strict staging criteria; for stage IV patients LDH within the institutional ULN must be documented within 4 weeks prior to randomization (M1c is not eligible) * NOTE: all subjects should be classified as IIIB, IIIC, M1a or M1b including subjects with disease recurrence after adequate surgical excision of the original primary melanoma; that is the treating team/physician investigator should review an overall TNM status (that includes primary tumor presentation and disease recurrence status) and provide a designation of IIIB, IIIC, M1a or M1b * Patients must be randomized within 84 days (12 weeks) of surgical resection; if more than one surgical procedure is required to render the patient disease-free, the patient must be randomized within 12 weeks of the last surgery * NOTE: patients with clinically positive lymph nodes for melanoma involvement or those with positive lymph nodes identified through lymphoscintigraphic and/or dye lymphographic techniques in the groin, axilla, or neck should have additional lymphadenectomy in those sites; the complete lymph node dissection procedure would be considered as the last surgery in counting the 84 days unless a subsequent surgical procedure(s) was clinically required to ensure the disease free status * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Given that serious adverse events may occur with ipilimumab and IFN-alpha and that these may impact a patient's wellbeing, it is possible that the occurrence of other serious adverse events (SAEs) may seriously impact an underlying state of mental depression and lead to suicidal ideation; therefore, patients should be carefully screened for depression at baseline and if there are indications or a history of depression it is strongly recommended that these patients be closely followed together with behavioral health or psychiatric medical support; patients with an established diagnosis of depression that, in the assessment of the investigator may make the administration of IFN-alpha or ipilimumab hazardous, should not be enrolled on this protocol; the risks and benefits of being treated with standard adjuvant IFN-alpha should be weighed very carefully in consultation with behavioral health or psychiatry * Due to the possible effect of treatment with ipilimumab on the immunologic response to infectious disease vaccines, patients must not have had any infectious disease vaccination (e.g., standard influenza, H1N1 influenza, pneumococcal, meningococcal, tetanus toxoid) within 4 weeks prior to randomization * 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 ipilimumab or HDI, in such a manner that the risk of pregnancy is minimized; 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 (e.g., vasectomy) should be considered to be of childbearing potential * Men of fathering potential and WOCBP must be using an adequate method of contraception to avoid conception/pregnancy throughout the study and for up to 26 weeks after the last dose of ipilimumab or HDI in such a manner that the risk of pregnancy is minimized; men or WOCBP who are unwilling or unable to strictly follow this requirement are not eligible * WOCBP are not eligible if they satisfy any of the following: * A positive pregnancy test at baseline * Pregnant or breastfeeding * White blood cell (WBC) \>= 3,000/uL (obtained within 4 weeks prior to randomization) * Absolute neutrophil count (ANC) \>= 1,500/uL (obtained within 4 weeks prior to randomization) * Platelets \>= 100 x 10\^3/uL (obtained within 4 weeks prior to randomization) * Hemoglobin \>= 10 g/dL (obtained within 4 weeks prior to randomization) * Serum creatinine =\< 1.5 mg/dL (obtained within 4 weeks prior to randomization) * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN (obtained within 4 weeks prior to randomization) * Serum bilirubin =\< 1.5 x ULN, (except patients with Gilbert's syndrome, who must have a total bilirubin less than 3.0 mg/dL) (obtained within 4 weeks prior to randomization) * No active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C due to the unknown effects of ipilimumab; patients must have negative testing for HIV, hepatitis B virus (HBV), hepatitis C virus (HCV) within 4 weeks prior to randomization Exclusion Criteria: * Patients must not have received any adjuvant treatment (chemotherapy, biotherapy, or limb perfusion) after the resection(s) that make(s) them eligible for this trial * NOTE: previous radiation therapy, including after the surgical resection, is allowed as long as 21 days have elapsed between the radiation and initiation of this adjuvant systemic therapy * Prior treatment with anti-cytotoxic T-lymphocyte antigen 4 (CTLA4) monoclonal antibodies or prior CTLA-4 inhibitor or agonist or prior clusters of differentiation (CD)137 agonist or prior interferon-alfa is not allowed; other forms of prior treatment for melanoma (e.g., aldesleukin \[IL-2\], anti-tumor vaccine, chemotherapy) are allowed if given before the resection(s) that make(s) the patient eligible for this trial, but these must have been completed at least 4 weeks prior to randomization * Patients must not have an active infection requiring current treatment with parenteral antibiotics * Patients must not have other significant medical, surgical, or psychiatric conditions or require any medication or treatment that in the opinion of the investigator may interfere with compliance, make the administration of ipilimumab or HDI hazardous or obscure the interpretation of adverse events (AEs), such as a condition associated with frequent diarrhea; patients with a baseline of frequent diarrhea (e.g. irritable bowel syndrome) are not eligible because of the difficulty in interpreting later expected GI toxicities that may lead to suboptimal management and complications * Patients must not have a documented history of inflammatory bowel disease (including ulcerative colitis and Crohn's disease) or diverticulitis (history of diverticulosis is allowed) * Patients must not have autoimmune disorders or conditions of immunosuppression that require current ongoing treatment with systemic corticosteroids (or other systemic immunosuppressants), including oral steroids (i.e., prednisone, dexamethasone) or continuous use of topical steroid creams or ointments or ophthalmologic steroids; a history of occasional (but not continuous) use of steroid inhalers is allowed; replacement doses of steroids for patients with adrenal insufficiency are allowed; patients who discontinue use of these classes of medication for at least 2 weeks prior to randomization are eligible if, in the judgment of the treating physician investigator, the patient is not likely to require resumption of treatment with these classes of drugs during the study * Exclusion from this study also includes patients with a history of symptomatic autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, Sjogren's syndrome, autoimmune vasculitis \[e.g., Wegener's granulomatosis\]); motor neuropathy considered of autoimmune origin (e.g., Guillain-Barre syndrome and Myasthenia Gravis); other central nervous system (CNS) autoimmune disease (e.g., poliomyelitis, multiple sclerosis) * Patients with autoimmune hypothyroid disease or type I diabetes on replacement treatment are eligible * Patients must not be prisoners or subjects who are compulsorily detained (involuntarily incarcerated) for treatment of either a psychiatric or physical (e.g., infectious) illness; this is due to concerns about subject safety and compliance with study procedures * Patients who have other current malignancies are not eligible; patients with other malignancies are eligible if they have been continuously disease free for \> 5 years prior to the time of randomization; patients with prior history at any time of any in situ cancer, lobular carcinoma of the breast in situ, cervical cancer in situ, atypical melanocytic hyperplasia or melanoma in situ are eligible; patients with prior history of basal or squamous skin cancer are eligible; patients who have had multiple primary melanomas are eligible * Women must not be pregnant or breast-feeding due to the unknown effects of ipilimumab and HDI on conception and the fetus; all females of childbearing potential must have a blood test or urine study during screening to rule out pregnancy * NOTE: a woman of childbearing potential (WOCBP) is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months); 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