Therapeutic Autologous Lymphocytes, Cyclophosphamide, and Aldesleukin in Treating Patients With Stage IV Melanoma

Inclusion Criteria: * Histopathological documentation of melanoma concurrent with the diagnosis of metastatic disease * Expression of HLA-A2, B44, or A3 as determined by Fred Hutchinson Cancer Research Center (FHCRC) human leukocyte antigen (HLA) typing lab * Zubrod performance status of 0-1 * Bi-dimensionally measurable disease by palpation on clinical exam, or radiographic imaging (X-ray, CT scan) * Normal cardiac stress test within 182 days prior to enrollment is required of all patients over 50 years old or those with an abnormal electrocardiogram (ECG), any history of cardiac disease, a family history of cardiac disease, hypercholesterolemia or hypertension * FOR LEUKAPHERESIS: * Pulse \> 45 or \< 120 * Weight \>= 45 kg * White blood cell count (WBC) \>= 3,000 * Temperature =\< 38C (=\< 100.4 F) * Hematocrit (HCT) \>= 30% * Platelets \>= 100,000 * FOR T CELL INFUSION: Patients must be willing and able to discontinue the use of all anti-hypertensive medications 24 hours prior to and during IL-2 therapy Exclusion Criteria: * Pregnant women, nursing mothers, men or women of reproductive ability who are unwilling to use effective contraception or abstinence; women of childbearing potential must have a negative pregnancy test within two weeks prior to entry * Serum creatinine \> 1.6 mg/dL or Creatinine clearance \< 75 ml/min * Serum glutamic oxaloacetic transaminase (SGOT) \> 150 IU or \> 3x upper limit of normal * Bilirubin \> 1.6 mg/dL * Prothrombin time \> 1.5 x control * Clinically significant pulmonary dysfunction, as determined by medical history and physical exam; patients so identified will undergo pulmonary functions testing and those with forced expiratory volume in one second (FEV1) \< 2.0 L or carbon monoxide diffusing capacity (DLco) (corr for Hgb) \< 75% will be excluded * Significant cardiovascular abnormalities as defined by any one of the following: * Congestive heart failure; * Clinically significant hypotension; * Symptoms of coronary artery disease; * Presence of cardiac arrhythmias on electrocardiograph (EKG) requiring drug therapy; * Ejection fraction \< 50 % (echocardiogram or multi gated acquisition scan \[MUGA\]) * Symptomatic central nervous system metastases greater than 1 cm at the time of therapy; patients with 1-2 asymptomatic, less than 1 cm brain/central nervous system (CNS) metastases without significant edema may be considered for treatment; if sub-centimeter CNS lesions are noted at study entry, than a repeat imaging will be performed if more than 3 weeks have elapsed from the last scan; patients will not be treated if CNS lesions are \> 1 cm or if patient is symptomatic from brain metastasis * Patients with active infections or oral temperature \> 38.2 C within 72 hours of study entry or systemic infection requiring chronic maintenance or suppressive therapy * Chemotherapeutic agents (standard or experimental), radiation therapy, or other immunosuppressive therapies less than 3 weeks prior to T cell therapy; (patients with bulky disease may undergo cytoreductive chemotherapy but treatment will be discontinued at least 3 weeks prior to T cell therapy) * Clinically significant autoimmune disorders or conditions of immunosuppression; patients with acquired immune deficiency syndrome (AIDS) or human immunodeficiency virus (HIV)-1 associated complex or known to HIV antibody seropositive or known to be recently polymerase chain reaction (PCR)+ for hepatitis are not eligible for this study; virology testing will be done within 6 months of T cell infusion; the severely depressed immune system found in these infected patients and the possibility of premature death would compromise study objectives * FOR T CELL INFUSION: Patients with active infections or oral temperature \> 38.2 C within 72 hours of study entry or systemic infection requiring chronic maintenance or suppressive therapy * FOR T CELL INFUSION: Chemotherapeutic agents (standard or experimental), radiation therapy, or other immunosuppressive therapies less than 3 weeks prior to T cell therapy * FOR T CELL INFUSION: Current treatment with steroids * FOR T CELL INFUSION: Patients must not be receiving any other experimental drugs within 3 weeks of the initiation of the protocol and must have recovered from all side effects of such therapy