In Vivo Persistence of Adoptively-Transferred TIL Cultured With Akti in People With Metastatic Melanoma

* INCLUSION CRITERIA * Measurable metastatic melanoma with at least one lesion that is resectable for TIL generation, plus one other lesion that can be measured. * Confirmation of diagnosis of metastatic melanoma by the Laboratory of Pathology of NCI. * Patients with 3 or fewer brain metastases that are less than 1 cm in diameter and asymptomatic are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for 1 month after treatment for the patient to be eligible. Patients with surgically resected brain metastases are eligible. * Prior therapy with at least one first line standard therapy including check point inhibitors such as pembrolizumab, nivolumab, or ipilimumab. * Note: Six weeks must have elapsed from the time of any of these prior antibody therapies that could affect an anti-cancer immune response, at the time the patient receives the preparative regimen to allow antibody levels to decline. * Note: Patients who have previously received ipilimumab and have documented GI toxicity must have a normal colonoscopy with normal colonic biopsies. * Greater than or equal to 18 years of age and less than or equal to 70 years of age. * Willing to sign a durable power of attorney. * Able to understand and sign the Informed Consent Document * Clinical performance status of ECOG 0 or 1. * Life expectancy of greater than three months. * Patients of both genders must be willing to practice birth control from the time of enrollment on this study and for up to four months after treatment. * Serology: * Seronegative for HIV antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus are less responsive to the experimental treatment and more susceptible to its toxicities.) * Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then patient must be tested for the presence of antigen by RT-PCR and be HCV RNA negative. * Women of child-bearing potential must have a negative pregnancy test because of the potentially dangerous effects of the treatment on the fetus. * Hematology: * Absolute neutrophil count greater than 1000/mm\^3 without the support of filgrastim * WBC greater than or equal to 3000/mm\^3 * Platelet count greater than or equal to 100,000/mm\^3 * Hemoglobin \> 8.0 g/dl * Chemistry: * Serum ALT/AST less than or equal to 2.5 times the upper limit of normal * Serum Creatinine less than or equal to 1.6 mg/dl * Total bilirubin less than or equal to 1.5 mg/dl, except in patients with Gilbert s Syndrome who must have a total bilirubin less than 3.0 mg/dl. * More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the preparative regimen, and patients toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo). Patients must have progressive disease after prior treatment. * Note: Patients may have undergone minor surgical procedures within the past 3 weeks, as long as all toxicities have recovered to grade 1 or less. * Six weeks must have elapsed from the time of any antibody therapy that could affect an anti cancer immune response, including anti-CTLA4 antibody therapy, at the time the patient receives the preparative regimen to allow antibody levels to decline. * Note: Patients who have previously received ipilimumab and have documented GI toxicity must have a colonoscopy with normal colonic biopsies. EXCLUSION CRITERIA * Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the treatment on the fetus or infant. * Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease). * Concurrent opportunistic infections (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immune competence may be less responsive to the experimental treatment and more susceptible to its toxicities). * Active systemic infections (for e.g.: requiring anti-infective treatment), coagulation disorders or other active major medical illnesses of the cardiovascular, respiratory or immune system, as evidenced by a positive stress thallium or comparable test, myocardial infarction, cardiac arrhythmias, obstructive or restrictive pulmonary disease. * Concurrent systemic steroid therapy. * History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine. * History of coronary revascularization or ischemic symptoms. * Documented LVEF of less than or equal to 45%, testing is required in patients with: * Age greater than or equal to 60 years old * Clinically significant atrial and or ventricular arrhythmias including but not limited to: atrial fibrillation, ventricular tachycardia, second or third degree heart block.