Aldesleukin and Pembrolizumab in Treating Patients With Stage III-IV Melanoma

Inclusion Criteria: * Histologic or cytologic diagnosis of cutaneous melanoma, mucosal melanoma, or melanoma of unknown primary that is considered unresectable (stage III) or metastatic (stage IV) * Be willing and able to provide written informed consent/assent for the trial * Have measurable disease evident on radiographs (preferred) or clinical examination; for this protocol, measurable disease is defined as at least one evaluable tumor that is at least 10 mm in longest dimension * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Patients must have a brain magnetic resonance imaging (MRI) or computed tomography (CT) (with and without contrast) 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 * Normal cardiac function; patients who have a history of heart disease, or who are over the age of 50 years must have a normal cardiac stress test within the prior 90 days * Normal lung function; patients who have extensive pulmonary metastases or any chronic pulmonary disease history must have pulmonary function testing demonstrating forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) \> 65% of predicted values * Absolute neutrophil count (ANC) \>= 1,500 /mcL * Platelets \>= 100,000 / mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases * Albumin \>= 2.5 mg/dL * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Subject meets institutional requirements for IL-2 therapy Exclusion Criteria: * Has primary ocular melanoma * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic immunosuppressive steroid therapy or any other form of systemic immunosuppressive therapy within 7 days prior to the first dose of trial treatment; exception: physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency is not considered systemic immunosuppressive steroid therapy * Has received previous high dose IL-2 therapy, any programmed death (PD)-1 blocking antibody (e.g. pembrolizumab, nivolumab), or any programmed death ligand (PD-L)1 blocking antibody in the metastatic setting; prior therapy with any PD-1 blocking antibody is allowed if given in the adjuvant setting and the last dose was \> 6 months prior to study entry; prior therapy with ipilimumab is allowed (in the adjuvant or metastatic setting); other prior therapy (in the adjuvant or the metastatic setting) is allowed, including targeted therapy, chemotherapy, or experimental therapy * Has a history of significant congestive heart failure or significant pulmonary disease * Has a known history of active TB (bacillus tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy and/or alopecia are exceptions to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of, or any evidence of active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy * Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed