NY-ESO-1-Specific T-cells in Treating Patients With Advanced NY-ESO-1-Expressing Sarcomas Receiving Palliative Radiation Therapy

Inclusion Criteria: INCLUSION CRITERIA FOR SCREENING: * Histopathological documentation of sarcoma * Patients must express NY-ESO-1 in their tumor by immunohistochemistry (IHC) (\> 5%) prior to leukapheresis * For leukapheresis, patients must meet the following criteria (any exceptions to this will require prior approval by the apheresis director and principal investigator \[PI\]): * Pulse \> 45 or \< 120 * Weight \>= 45 kg * Temperature =\< 38° Celsius (C) (=\< 100.4° Fahrenheit \[F\]) * White blood cell count (WBC) \>= 2,000 * Hematocrit (HCT) \>= 30% * Platelets \>= 75,000 INCLUSION CRITERIA FOR TREATMENT: * A diagnosis of a metastatic or unresectable sarcoma * Patient must have a biopsy-accessible tumor to be radiated * Patient must have consulted with a radiation oncologist who is planning radiation; their radiation oncologist should have documented plans to administer a dose of at least 30 Gy in 5 or fewer fractions * Human leukocyte antigen (HLA) type A0201 or A2402 * Zubrod (Eastern Cooperative Oncology Group \[ECOG\]) performance status of '0-2' * All patients must have an electrocardiogram (ECG) within 2 weeks of starting conditioning * All patients must have an echo or multigated acquisition (MUGA) scan showing ejection fraction (EF) \> 50% and normal troponin and creatine kinase MB (CK MB) performed within 90 days of starting treatment Exclusion Criteria: EXCLUSION CRITERIA FOR SCREENING: * Patients who do not meet the above inclusion criteria will not receive leukapheresis EXCLUSION CRITERIA FOR TREATMENT: * Patients with a history of proven myocarditis, pericarditis, or endocarditis * Pregnant women, nursing women, men and women of reproductive ability who are unwilling to use effective contraception or abstinence; women of childbearing potential must have a negative pregnancy test within two weeks prior to study entry * Inadequate renal function as indicated by serum creatinine \>= 1.5 times the upper limit of normal * Inadequate liver function as indicated by total bilirubin \>= 1.5 times the upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \>= 2.5 times the upper limit of normal * Active symptomatic congestive heart failure * Clinically significant hypotension * Newly diagnosed cardiac arrhythmia; patients with an arrhythmia that has been stable for at least 3 months will be allowed to participate * Known untreated central nervous system (CNS) metastasis * Patients with systemic infections requiring antibiotics or chronic maintenance/suppressive therapy * Patients receiving systemic anticancer therapy (chemotherapy, "biologics", immunotherapy) less than 2 weeks prior to starting radiation * Clinically significant autoimmune disorders requiring on-going systemic immune-suppression for control * Patients with acquired immunodeficiency syndrome (AIDS) or who are known to be human immunodeficiency virus (HIV) positive are not eligible for this study; testing may have been done up to 3 months prior to treatment * Current treatment with steroids * Known infection with hepatitis B virus (HBV) and hepatitis C virus (HCV); testing may have been done up to 3 months prior to treatment