Aldesleukin With or Without Ziv-Aflibercept in Treating Patients With Stage III-IV Melanoma That Cannot Be Removed by Surgery

Inclusion Criteria: * Patients must have histologically or cytologically confirmed metastatic melanoma (includes American Joint Committee on Cancer \[AJCC\] stage IV or advanced/inoperable stage III; also includes patients with a history of lower stage melanoma and subsequent recurrent metastatic disease that is either locally/regionally advanced/inoperable disease or distant metastases) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 10 mm with computed tomography (CT) scan or clinically (must be measurable with calipers) according to RECIST version 1.1 * Patients must be free of brain metastasis by contrast-enhanced 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) * A patient may be treatment naïve; however, up to two prior regimens for metastatic melanoma are allowed; prior adjuvant interferon (IFN)-alpha is allowed; no prior therapy with bevacizumab, aflibercept or interleukin-2 (IL-2) * Patients must not have received systemic therapy or radiotherapy within the preceding 4 weeks; patients must have recovered from adverse events due to agents administered more than 4 weeks earlier * Patients must be at least 4 weeks from major surgery and have fully recovered from any effects of surgery, and be free of significant detectable infection * For patients who have received prior anti-cytotoxic T-lymphocyte antigen (CTLA)4 monoclonal antibody therapy (ipilimumab or tremelimumab), there is a risk of bowel perforation with IL-2 therapy; therefore, for these patients if they have a history of colitis or diarrhea during anti-CTLA4 monoclonal antibody therapy, they should have a formal evaluation by a gastroenterologist and a colonoscopy should be considered to demonstrate the absence of active bowel inflammation before initiating IL-2 therapy on this protocol * Life expectancy of greater than 3 months in the opinion of the investigator * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 (Karnofsky \> 70%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine within 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine level above institutional normal * Urine protein should be screened by urinalysis for urine protein creatinine ratio (UPCR); for UPCR \> 1, a 24-hour urine protein should be obtained and the level should be \< 500 mg * Patients on full-dose anticoagulants (e.g., warfarin) with prothrombin time (PT) international normalized ratio (INR) \> 1.5 are eligible provided that both of the following criteria are met: * The patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * The patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * Forced expiratory volume (FEV) 1 \> 2.0 liters or \> 75% of predicted for height and age (pulmonary function test \[PFTs\] are required for patients over 50 years old or with significant pulmonary or smoking history) * No evidence of congestive heart failure, symptoms of coronary artery disease, myocardial infarction less than 6 months prior to entry, serious cardiac arrhythmias, or unstable angina * Patients who are over 40 years old or have had previous myocardial infarction greater than 6 months prior to study entry or have significant cardiac family history (coronary artery disease \[CAD\] or serious arrhythmias) will be required to have a negative or low probability cardiac stress test (for example, thallium stress test, stress multi-gated acquisition scan \[MUGA\], stress echocardiography \[echo\], or exercise stress test) for cardiac ischemia within 8 weeks prior to registration * An echocardiogram should be performed at baseline in all patients; ejection fraction (EF) from baseline echocardiogram must be within the institutional limits of normal as determined by the reading cardiologist; if the baseline cardiac stress test incorporates an echocardiogram, then this will not need to be done again at baseline * No history of cerebrovascular accident or transient ischemic attacks within the past 6 months * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for at least 6 months after completion of study therapy; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Women should not be lactating and, if of childbearing age, should have a negative pregnancy test (beta-human chorionic gonadotropin \[b-HCG\] test; serum or urine, minimum sensitivity 25 IU/L or equivalent units of b-HCG) within two week of registration in the study * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * Patients with brain metastases should be excluded from this clinical trial except as noted above * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies, and patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to other agents used in the study * Serious or non-healing wound, ulcer, or bone fracture * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days of treatment * Patients with the following invasive procedures: * Major surgical procedures, open biopsy or significant traumatic injury within 28 days prior to day 1 therapy * Anticipation of need for major surgical procedures during the course of the study * Minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to day 1 of therapy; central venous catheter placements are permitted to be completed 7 or more days prior to day 1 of therapy; however, peripherally inserted central catheter (peripherally inserted central catheter \[PICC\] or PIC line) may be placed at any time prior to or during therapy * Patients with clinically significant cardiovascular or cerebrovascular disease: * History of cerebrovascular accident or transient ischemic attack within past 6 months * Uncontrolled hypertension, defined as blood pressure \> 150/100 mm Hg or systolic blood pressure (BP) \> 180 mm Hg if diastolic blood pressure \< 90 mm Hg, on at least 2 repeated determinations on separate days within past 3 months * Myocardial infarction, coronary artery bypass graft (CABG) or unstable angina within the past 6 Months * New York Heart Association grade III or greater congestive heart failure, serious cardiac arrhythmia requiring medication, unstable angina pectoris within past 6 months * Clinically significant peripheral vascular disease within past 6 months * Pulmonary embolism, deep vein thrombosis (DVT), or other thromboembolic event within past 6 months * History of tumor-related or other serious hemorrhage, bleeding diathesis, or underlying coagulopathy * PT INR \> 1.5 unless the patient is on full-dose warfarin * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * 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 a prior history of basal cell or squamous cell skin cancer are eligible; patients who have had multiple primary melanomas 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 (i.e., prednisone, dexamethasone) or continuous use of topical steroid creams or ointments or ophthalmologic steroids or steroid inhalers * If a patient had been taking steroids, at least 2 weeks must have passed since the last dose