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

Inclusion Criteria: * FOR LEUKAPHERESIS: * Pulse \> 45 or \< 120 * Weight \>= 45 kg * Temperature =\< 38 Celsius (C) (=\< 100.4 Fahrenheit \[F\]) * White blood cells (WBC) \>= 3000 * Hematocrit (HCT) \>= 30% * Platelets \>= 100,000 * FOR T CELL INFUSION: * Histopathological documentation of melanoma concurrent with the diagnosis of metastatic disease * Tumor expression of MART-1 (2+ staining or \> 25%) by immunohistochemistry (IHC) * Able to tolerate high-dose cyclophosphamide * Expression of human leukocyte antigen (HLA)-A2 * Zubrod performance status of 0-1 * Bi-dimensionally measurable disease by palpation on clinical exam, or radiographic imaging (X-ray, computed tomography \[CT\] 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 or hypertension 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 (CrCl) \< 75 ml/min (calculated: Cockcroft and Gault equation: CrCl = (140 - age) x ideal body weight (IBW)/(serum creatinine \[Scr\] x 72) (x 0.85 for females) * Serum glutamic oxaloacetic transaminase (SGOT) \> 150 IU or \> 3 x upper limit of normal * Direct bilirubin \> 1.0 mg/dL * Prothrombin time \> 1.5 x control (in the absence of systemic anticoagulation) * Clinically significant pulmonary dysfunction, as determined by medical history and physical exam; patients so identified will undergo pulmonary functions testing at the discretion of their primary physician * 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 electrocardiogram (EKG) requiring drug therapy * Symptomatic central nervous system metastases greater than 1 cm at time of therapy; patients with 1-2 asymptomatic, less than 1cm brain/central nervous system (CNS) metastases without significant edema may be considered for treatment; if sub-centimeter CNS lesions are noted at study entry, then 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 immunodeficiency syndrome (AIDS) or human immunodeficiency virus (HIV)-1 associated complex or known to HIV antibody seropositive or known to be recently polymerase chain reaction positive (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 * Patients who, in the opinion of their physician, are not clinically suited for high-dose cytoxan