Ipilimumab With or Without High-Dose Recombinant Interferon Alfa-2b in Treating Patients With Stage III-IV Melanoma That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have unresectable stage III or stage IV melanoma, either initial presentation or recurrent, that is of cutaneous origin or unknown primary origin and that is histologically diagnosed * No more than one prior systemic therapeutic regimen for unresectable stage III or stage IV melanoma; this includes chemotherapy, biologic therapy, biochemotherapy, or investigational treatment; this does not include any therapies given in the adjuvant setting; however, patients are excluded if they have a history of prior treatment for melanoma (either adjuvant or metastatic disease) with ipilimumab or other cytotoxic T-lymphocyte antigen 4 (CTLA-4) inhibitor, or prior interferon-alpha treatment for metastatic disease (history of adjuvant interferon-alpha is allowed); there should be a 4-week washout period between last treatment administration and initiation of study therapy * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * 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 must not have an active infection requiring current treatment with parenteral antibiotics * Patients must not have a history of inflammatory bowel disease or diverticulitis (history of diverticulosis is allowed) * 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; one exception are patients treated with a curative intent and are continuously disease free for \> 3 years; these patients would be considered eligible: * 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 Clark I melanoma in situ are eligible * Patients with prior history of basal or squamous skin cancer are eligible * 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 (e.g., 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 * 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 * Women must not be pregnant or breast-feeding; 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: 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); for the purposes of this study, post-menopause is defined as: * Amenorrhea \>= 24 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 (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 or must abstain from sexual intercourse 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 * White blood cells (WBC) \>= 3000/uL * Absolute neutrophil count (ANC) \>= 1500/uL * Platelets \>= 100 x 10\^3/uL * Hemoglobin \>= 10 g/dL * Serum creatinine =\< 1.8 mg/dl * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) for patients with liver metastases and =\< 2.0 x ULN for patients without liver metastases * Serum bilirubin \< 2 x ULN for patients with liver metastases and =\< 1.5 x ULN for patients without liver metastases, (except patients with Gilbert's syndrome, who must have a total bilirubin \< 3.0 mg/dL) * No active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C * Patients must be free of brain metastasis by contrast-enhanced computed tomography (CT)/magnetic resonance imaging (MRI) scans within 4 weeks prior to enrollment; if known to have prior brain metastases, must not have evidence of active brain disease after definitive therapy (surgery, radiation therapy or stereotactic radiosurgery) on two successive MRI evaluations at least 3 months apart (one of which is =\< 4 weeks prior to starting the study drugs) * All sites of disease must be evaluated within 4 weeks prior to randomization; patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1