Isolated Limb Perfusion With Melphalan in Treating Patients With Stage IIIB-IV Melanoma or Sarcoma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * The patient must have histological-proven primary or recurrent extremity melanoma (or other skin cancer including but not limited to Merkel cell carcinoma) or sarcoma, stage IIIB, IIIC, or IV (American Joint Committee on Cancer \[AJCC\] staging must be documented in patient's medical record, as determined by computed tomography \[CT\] of the chest, abdomen and pelvis, and/or whole body positron emission tomography \[PET\] scan, within six weeks prior to administration of study drug) * Patients with stage IV disease who have high tumor burden and extensive symptomatic extremity disease * Patients with stage IIIC disease must either have had regional lymph nodes previously removed or will have them removed either at the time of regional treatment or soon thereafter * Disease to be treated by ILP must be unresectable and distal to the planned site of tourniquet placement (which for the leg is generally the apex of the femoral triangle, or for the arm is distal to the deltoid insertion) * Patient's disease must be bi-dimensionally measurable by caliper or radiological method as defined in the Response Evaluation Criteria in Solid Tumors (RECIST) criteria (RECIST updated version 1.1); lesional tissue not necessary for diagnostic or other clinical purposes may be designated prospectively for research tissue banking * Hemoglobin \>= 8.0 g/dl * White blood count (WBC) of \>= 2000 m\^3 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x the ULN * Creatinine =\< 1.5 x ULN * Patient must have a palpable femoral/radial pulse in the affected extremity * Patients must have a life expectancy of \> 6 months * Patient or the patient's legally acceptable representative must provide a signed and dated written informed consent prior to registration and any study-related procedures * Patient or the patient's legally acceptable representative must provide written authorization to allow the use and disclosure of their protected health information at any institution subject to United States Health Insurance Portability and Accountability Act (US HIPAA) regulations; NOTE: This may be obtained in either the study-specific informed consent or in a separate authorization form and must be obtained from the patient prior to study registration Exclusion Criteria: * Cardiac disease: congestive heart failure \> class II New York Heart Association (NYHA); patients must not have unstable angina (angina symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months * Known brain metastasis; patients with neurological symptoms must undergo a CT scan/magnetic resonance imaging (MRI) of the brain to exclude brain metastasis * Known human immunodeficiency virus (HIV) infection or chronic hepatitis B or C * Active clinically serious infection \> Common Terminology Criteria for Adverse Events (CTCAE) grade 2 * Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Pulmonary hemorrhage/bleeding event \>= CTCAE grade 2 within 4 weeks of ILP/isolated limb infusion (ILI); any other hemorrhage/bleeding event \>= CTCAE grade 3 within 4 weeks ILP/ILI * Major surgery or significant traumatic injury within 30 days of ILI/ILP * Evidence or history of bleeding diathesis or coagulopathy * Antineoplastic therapy, radiotherapy, or any other investigational drug within 30 days prior to first study drug administration * Patients with symptoms or signs of vascular insufficiency; specifically, patients with any history of blood clots or lifestyle altering ischemic peripheral vascular disease will be excluded * History of allergic reactions and/or hypersensitivity to melphalan * Psychiatric conditions or diminished capacity that could compromise the giving of informed consent, or interfere with study compliance * Pregnant or nursing women are not eligible for this study * Unable to return at the regular required intervals for reassessment, or study drug administration * Patients with known heparin induced thrombocytopenia