NY-ESO-1 Specific T Cells After Cyclophosphamide in Treating Patients With Advanced Synovial Sarcoma or Myxoid/Round Cell Liposarcoma

Medical history including histopathological documentation of sarcoma

Informed consent and Health Insurance Portability and Accountability Act (HIPAA) signing

CRITERIA FOR LEUKAPHERESIS:

NY-ESO-1 expression in tumor by immunohistochemistry (IHC) is not required prior to screening consent; however, patients must have NY-ESO-1 expression to proceed with the leukapheresis; additionally patients must also meet the following criteria to proceed with leukapheresis (any exceptions to this will require prior approval by the Apheresis director and Principal Investigator):

Physical exam and Karnofsky performance status

Laboratory evaluation:

Complete blood count (CBC), differential and platelet count

Basic metabolic and hepatic function panels

Puget Sound Blood Center Recipient Donor Battery Panel

Pregnancy test for females of child-bearing potential

Pulse \> 45 and \< 120

Weight \>= 45 kg

Temperature =\< 38 Celsius (C) (=\< 100.4 Fahrenheit \[F\])

White blood cell (WBC) \>= 2,000

Hematocrit (HCT) \>= 30%

Platelets \>= 75,000

Research blood including 40 mL of blood in a heparinized tube for peripheral blood mononuclear cell (PBMC) collection and 10 mL of blood for serum collection (generally in a red top tube) within 30 days of leukapheresis collection

A diagnosis of synovial sarcoma or myxoid/round cell liposarcoma

Patients must have "advanced disease"; usually, this will mean metastatic disease; this may also be multiply recurrent disease or locally advanced disease; locally advanced disease is defined for this study as disease where a mutilating surgery is required and the patient is more likely than not to die of their disease despite an aggressive operation; patients with metastatic disease that has been resected or radiated are allowed to participate; Response Evaluation Criteria in Solid Tumors (RECIST) evaluable disease is not necessary for participation

NY-ESO-1 positive by IHC (for this study, even a small level of positivity is acceptable); for patients with \< 5% NY-ESO-1 by IHC positivity, the level of staining should be discussed with the patient and they should be informed that this will likely effect the efficacy of the therapy; this conversation must be documented in the patient's medical chart

Human leukocyte antigen (HLA)-A0201 or HLA-A2402

Zubrod performance status of '0-1'

All patients must have an electrocardiogram (ECG) within 2 weeks of starting conditioning

All patients must have a stress test within 6 months of starting treatment showing no evidence of cardiac ischemia

All patients must have an echo or multi gated acquisition scan (MUGA) scan showing ejection fraction (EF) \> 50% and normal troponin and creatine kinase (CK) myoglobin binding (MB) (echo may be done at the time of stress test as a stress echo); within 6 months of starting treatment; however if the patient has received cardiotoxic chemotherapy such as Adriamycin, they must have had an echo or MUGA scan since completing this treatment

If there is a patient with an NY-ESO-1 expressing soft tissue sarcoma who would be otherwise eligible for the trial, which is either not synovial sarcoma (SS) or myxoid/round cell liposarcoma (MRCL) or there is controversy about the diagnosis, eligibility will be decided by the PI

Patients must have NY-ESO-1 specific cells already produced or in production; these cells may be either in the process of their final expansion (for fresh infusion) or expanded and frozen at the time of enrollment

What this study is about