Genetically Modified Therapeutic Autologous Lymphocytes Followed by Aldesleukin in Treating Patients With Stage III or Metastatic Melanoma

Inclusion Criteria: * TURNSTILE I INCLUSION CRITERIA: * Patients must have metastatic melanoma or stage III in-transit, subcutaneous, or regional nodal disease (Turnstile I) * Patients must have a lesion amenable to resection for the generation of TIL (Turnstile I) * Patients must receive a magnetic resonance imaging (MRI)/computed tomography (CT)/positron emission tomography (PET) of the brain within 6 months of signing informed consent; if new lesions are present, patient must have definitive treatment; principal investigator (PI) or his designee should make final determination regarding enrollment (Turnstile I) * Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0-2 within 30 days of signing informed consent (Turnstile I) * Patients previously treated with immunotherapy, targeted therapy, or no therapy will be eligible; patients receiving cytotoxic agents will be evaluated by the PI or his designee * Patients with a negative pregnancy test (urine or serum) must be documented within 14 days of screening for women of childbearing potential (WOCBP); a WOCBP has not undergone a hysterectomy or who has not been naturally postmenopausal for at least 12 consecutive months (Turnstile I) * CHEMOTHERAPY/CELL INFUSION INCLUSION CRITERIA: * Patients must have adequate TIL available (Turnstile II) * Patients must have at least one biopsiable and measurable metastatic melanoma lesions \>= 1 cm (Turnstile II) * Patients may have brain lesions which measure =\< 1 cm each (Turnstile II) * Patients of both genders must practice birth control for four months after receiving the preparative regimen (lymphodepletion) and continue to practice birth control throughout the study; patients must have a documented negative pregnancy test (urine or serum) for women who have menstruation in the past 12 months and without sterilization surgery (Turnstile II) * Unless surgically sterile by bilateral tubal ligation or vasectomy of partner(s), the patient agrees to continue to use a barrier method of contraception throughout the study such as: condom, diaphragm, hormonal, intrauterine device (IUD), or sponge plus spermicide; abstinence is an acceptable form of birth control (Turnstile II) * Pregnancy testing will be performed within 14 days prior to treatment (Turnstile II) * Clinical performance status of ECOG 0-2 within 14 days of lymphodepletion (Turnstile II) * Absolute neutrophil count greater than or equal to 1000/mm\^3 (Turnstile II) * Platelet count greater than or equal to 100,000/mm\^3 (Turnstile II) * Hemoglobin greater than or equal to 8.0 g/dl (Turnstile II) * Serum alanine transaminase (ALT) less than three times the upper limit of normal (Turnstile II) * Serum creatinine less than or equal to 1.6 mg/dl (Turnstile II) * Total bilirubin less than or equal to 2.0 mg/dl, except in patients with Gilbert's syndrome who must have a total bilirubin less than 3.0 mg/dl (Turnstile II) * A stress cardiac test (stress thallium, stress multigated acquisition \[MUGA\] scan, dobutamine echocardiogram or other stress test that will rule out cardiac ischemia) within 6 months of lymphodepletion (Turnstile II) * Forced expiratory volume in 1 second (FEV1) \> 65% of predicted within 6 months of lymphodepletion (Turnstile II) or * Forced vital capacity (FVC) \> 65% of predicted within 6 months of lymphodepletion (Turnstile II) * MRI/CT/PET of the brain within 30 days of lymphodepletion Exclusion Criteria: * Active systemic infections requiring intravenous antibiotics, coagulation disorders or other major medical illnesses of the cardiovascular, respiratory or immune system; PI or his designee shall make the final determination regarding appropriateness of enrollment (Turnstile I) * Patients who are pregnant or nursing (Turnstile I) * CHEMOTHERAPY/CELL INFUSION EXCLUSION CRITERIA: * Has had prior systemic cancer therapy within the past four weeks at the time of the start of the lymphodepletion regimen (Turnstile II) * Women who are pregnant will be excluded (Turnstile II) * Any active systemic infections requiring intravenous antibiotics, coagulation disorders or other major medical illnesses of the cardiovascular, respiratory or immune system, such as abnormal stress thallium or comparable test, myocardial infarction, cardiac arrhythmias, obstructive or restrictive pulmonary disease; PI or his designee shall make the final determination regarding appropriateness of enrollment (Turnstile II) * Any form of primary or secondary immunodeficiency; must have recovered immune competence after chemotherapy or radiation therapy as evidenced by lymphocyte counts (\> 500/mm\^3), white blood cell (WBC) (\> 3,000/mm\^3) or absence of opportunistic infections (Turnstile II) * Requires no steroids within 4 weeks and have not used topical or inhalational steroids in the past 2 weeks prior to lymphodepletion; the exception being patients on chronic physiologic dose of steroid (Turnstile II) * Presence of a significant psychiatric disease, which in the opinion of the principal investigator or his designee, would prevent adequate informed consent or render immunotherapy unsafe or contraindicated (Turnstile II)