Proof of Concept of TBio-4101, Lymphodepleting Chemo, IL-2 for Relapsed/Refractory Melanoma

Inclusion Criteria: * Participants must have histologically confirmed, unresectable or metastatic melanoma as follows: * Cutaneous, non-acral, melanoma (including melanoma of unknown primary) * Cutaneous acral melanoma * Mucosal melanoma * Ocular melanoma (including uveal, iris, conjunctival melanoma) * Participants must have failed, be refractory to, or unable to tolerate standard of care in the opinion of the Investigator. For participants with cutaneous non-acral melanoma, standard of care therapy includes a PD-1/L1 inhibitor, a CTLA-4 inhibitor, and if BRAF V600 activating mutation positive, a BRAF ± MEK inhibitor. Note: if treatment failure occurs during adjuvant therapy or within 6 months of adjuvant therapy completion, this will count as a failure of the applicable regimen as noted above. * Any systemic therapy, including anti-cancer monoclonal antibodies, must have been completed at least 4 weeks from the start of lymphodepleting therapy (except for bridging therapy as defined below), and any prior therapy-related AEs must have resolved to Grade ≤ 1 except for alopecia and vitiligo. Neuropathy must have resolved to Grade ≤ 2. * Participants must be between the ages of 18 and 75 years old. Additionally, participants who are ≥ 60 years of age must undergo a cardiology evaluation including a cardiac stress test after which they must be deemed to be low/acceptable risk. * ECOG performance status of 0 or 1 * Participants must have adequate organ and marrow function as defined below: 1. Absolute neutrophil count ≥ 1,500/mcL (non-growth factor supported) 2. Platelet count ≥ 100,000/mcL 3. Hemoglobin ≥ 8.0 g/dL 4. AST (SGOT)/ALT (SGPT) ≤ 3 times the institutional ULN; ≤ 5 times ULN if patient has liver metastasis 5. Cockcroft-Gault estimated GFR ≥ 50 mL/min (creatinine) 6. Total bilirubin ≤ 2.0 mg/dL (except in patients with Gilbert's Syndrome where the bilirubin must be ≤ 3 mg/dL) * Seronegative for Human immunodeficiency virus (HIV) antibody, hepatitis B surface antigen, and hepatitis C (HCV) antibody (if HCV antibody positive, must be tested for HCV RNA, which must be negative to be eligible) * Participants with brain metastases are eligible provided that the brain metastases have been successfully treated with stereotactic radiosurgery or resection and clinically stable for at least 1 month. * Participants who have not undergone prior TIL harvest (i.e., the patient was not enrolled in the Banked TIL protocol MCC# \<TBD\>) must have at least 1 cm of tumor amenable for resection for TIL generation, in addition to, having at least one target lesion that can be used for response assessment by RECIST 1.1 criteria after TIL harvest. * Participants who have undergone prior TIL harvest with the banking protocol (MCC# \<TBD\>) must have adequate numbers of cryopreserved TIL after the pre-REP to meet criteria for proceeding with TBio-4101 therapy. * Participants must be willing and able to undergo an apheresis procedure * Women of child-bearing potential must have a negative pregnancy test * The effects of TBio-4101 on the developing human fetus are unknown. For this reason and because TIL agents, as well as other therapeutic agents used in this trial including IL-2 are known to be teratogenic, both males and females of child-bearing potential must be willing to practice birth control starting with screening through 1 year after the last study drug is administered for females or 6 months for males. Note: Women of child-bearing potential must have a negative serum pregnancy test. * Contraception requirement: * To prevent pregnancy, patients who are able to conceive or father children must use a highly effective contraception method during sexual activity starting with Screening through 1 year after the last study drug is administered for females or 6 months for males. Based on their mechanisms of action, the NMA-LD chemotherapy, aldesleukin (IL-2), can cause fetal harm when administered to a pregnant woman. Effects of TBio-4101 on fetal development are unknown. * Definition of Non-Reproductive Potential: For this trial, male patients will be considered to be of non-reproductive potential if they have azoospermia (whether due to having had a vasectomy or due to an underlying medical condition). Female patients will be considered of non-reproductive potential if they are either: (a) postmenopausal (defined as at least 12 months with no menses without an alternative medical cause; in women \< 45 years of age, a high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a post-menopausal state in women not using hormonal contraception or hormonal replacement therapy. In the absence of 12 months of amenorrhea, a single follicle FSHH measurement is insufficient); (b) Or have had a hysterectomy and/or bilateral oophorectomy, bilateral salpingectomy or bilateral tubal ligation/occlusion, at least 6 weeks prior to screening; (c) Or has a congenital or acquired condition that prevents childbearing. * Definition of Highly Effective Contraception: The following are examples of acceptable contraception methods to prevent pregnancy. This list may not be comprehensive for all regions, so the Investigator must discuss sexual activity and contraception usage with the patient. Hormonal contraceptive: oral contraceptive pill (estrogen/progestin pill or progestin-only pill), contraceptive skin patch, vaginal contraceptive ring, or subcutaneous contraceptive injection, Intrauterine device (IUD), Intrauterine hormone releasing system (IUS), Bilateral tubal occlusion, Vasectomized partner. * Should a woman become pregnant or suspect she is pregnant while she or her partner are participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants, regardless of age, who have a current or past medical history of ischemic heart disease, or clinically significant atrial or ventricular rhythm abnormality are excluded unless they undergo a cardiac stress test and cardiology clearance examination and are determined to be low or acceptable risk. Note: Participants with any clinically significant cardiac wall movement abnormality are excluded. * Participants who have received prior cell therapy. * Participants with either a primary immunodeficiency disorder (i.e., severe combined immunodeficiency syndrome) or acquired immunodeficiency disorders (such as HIV/AIDS) * Pregnant women are excluded from this study because the agents used in this study have teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with TBio-4101 or the other agents in the study, breastfeeding should be discontinued if the mother is enrolled in the study. * Participants taking systemic steroid therapy (other than replacement therapy) or therapy with any immunosuppressive medications such as mycophenolate mofetil (MMF). Participants who require dapsone for pneumocystis pneumonia (PCP) prophylaxis during TIL therapy are eligible. * Participants who have a history of severe immediate hypersensitivity reaction to the study agents including cyclophosphamide, fludarabine, or aldesleukin/ IL-2 or any of their constituents * Participants with a left ventricular ejection fraction (LVEF) ≤ 45% or New York Heart Association (NYHA) functional classification \> 1 * Forced expiratory volume (FEV1) ≤ 60% of predicted value and DLCO (corrected) \< 60% of predicted value * Participants who, in the opinion of the Investigator, have a medical condition that would subject the patient to prohibitive risk by participation in this study, or who may be unable to safely complete the apheresis, tumor harvest, lymphodepletion regimen, TIL infusion, or aldesleukin/ IL-2 administration * Participants with active infections requiring parenteral antibiotics * Participants with autoimmune disease currently or within the past 6 months requiring systemic treatment with immunosuppressive doses of corticosteroids (\>10 mg of prednisone-equivalent daily dosing), immunosuppressive biologic agents, or disease modifying antirheumatic drug agents (DMARDs). Note: Participants with autoimmune thyroiditis on replacement thyroid medication are eligible. * Participants requiring chronic anti-coagulant therapy that cannot either be discontinued or changed to an anti-coagulant such as a low molecular weight heparin, which has a relatively short half-life, if clinically indicated during the period of thrombocytopenia resulting from the lymphodepletion regimen * Has evidence of impeding perforation, obstruction or bleeding (requiring transfusion) due to the tumor.