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