A2-ESO-1 TCR-Engineered T Cells for Relapsed/Refractory Advanced or Metastatic NY-ESO-1 Overexpression Positive Triple Negative Breast Cancer

Inclusion Criteria: * Female aged \>= 18 years * Histologically confirmed advanced or metastatic TNBC that have relapsed on or are refractory to 2 or more lines of standard-of-care therapy. TNBC is defined as estrogen receptor (ER) and progesterone receptor negative (\< 10% immunohistochemistry \[IHC\] staining) and HER2 negative (IHC 1+ or 0 AND/OR in situ hybridization negative based on: * Single-probe average HER2 copy number \< 4.0 signals/cell * Dual-probe HER2/CEP17 ratio \< 2.0 with an average HER2 copy number \< 4.0 signals/cell) * HLA-A2+ and tumoral overexpression of NY-ESO-1 (2 to 3+ IHC staining in \> 50% of cells) * Have measurable disease based on RECIST 1.1 * Life expectancy \>= 6 months * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Hemoglobin \>= 9.0 g/dL (transfusions permitted) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Creatinine (Cr) \< 2 x upper limit of normal (ULN), and Cr clearance (CrCl) \>= 50 mL/min by Cockcroft and Gault * Alanine transaminase (ALT) and aspartate transaminase (AST) \< 2 x ULN (Patients with liver metastases whose ALT/AST are \< 5 x ULN are eligible for enrollment) * Bilirubin \< 2 x ULN * Lymphocyte count \>= 500/uL * Cardiac left ventricular ejection fraction (LVEF) \>= 50% * Negative serum pregnancy (human chorionic gonadotropin \[beta-hCG\]) test within 7 days of leukapheresis for women of childbearing potential (WOCBP). WOCBP must be willing to use a highly effective method of contraception for the course of the study through 90 days after A2-ESO-1 TCR-engineered T cell infusion * Willing and able to provide written informed consent for the study * Willing to provide biopsy tissues and blood samples as required by the study Exclusion Criteria: * Radiation therapy, chemotherapy, or non-cytotoxic investigational agent within 2 weeks of leukapheresis * Received cyclophosphamide within the past 4 months * Evidence of New York Heart Association class III or greater cardiac disease * History of myocardial infarction, stroke, ventricular arrhythmia, or symptomatic conduction abnormality within the past 12 months * History of congenital QT prolongation * Absolute QT interval of \> 470 msec in the presence of \> 4.0 mEq/L potassium and \> 1.8 mg/dL magnesium * Brain or leptomeningeal metastases * Females who are pregnant or breastfeeding * Hypersensitivity or intolerance to cyclophosphamide, fludarabine, IL-2, or their components * History of clinically significant gastrointestinal bleeding, gastric or intestinal ulceration, or perforation within 6 months of enrollment. * Any severe and/or uncontrolled medical conditions or other conditions that could affect participation in the study, such as severely impaired lung function, any active (acute or chronic) or uncontrolled infection/disorders, and non-malignant medical illnesses that are uncontrolled or whose control may be jeopardized by the study treatment * Current use of medications that interact with or compromise the immune system such as steroid doses \> 10 mg/day prednisone or equivalent daily within 2 weeks before leukapheresis * History of immunodeficiency disease or autoimmune disease, with exceptions such as Hashimoto's thyroiditis / hypothyroidism, or controlled Type 1 diabetes * Have any active and uncontrolled infection. * Active hepatitis B (as defined as positive hepBsAntigen or detectable hepatitis B DNA) or hepatitis C infection. Patients who are hepatitis B surface Antigen negative and have a negative hep B DNA are allowed. If hepatitis C antibody test is positive, then patients must be tested for the presence of antigen by RT-PCR and be HCV RNA negative. Patients with laboratory evidence of cleared hepatitis B or C infection may enroll. Patients with no prior history of hepatitis B infection who have been vaccinated against hepatitis B and who have a positive antibody against hepatitis B surface antigen as the only evidence of prior exposure may enroll. Patients with a history of hepatitis C infection may be eligible if they have completed antiviral treatment and show no detectable HCV RNA for 6 months prior to enrollment. * Human immunodeficiency virus (HIV) infection or seropositive for HIV antigens * Concurrent use of any complementary or alternative medicines * Unwilling or unable to comply with the study protocol * Prior major surgery that requires general anesthesia must be completed at least 4 weeks before leukapheresis and surgery that requires local anesthesia (except for study tissue sample collection) must be completed at least 2 weeks before leukapheresis and surgery that requires local anesthesia (except for study tissue sample collection) must be completed at least 2 weeks before leukapheresis