Neoadjuvant Lurbinectedin and Preoperative Radiation for Treating Soft Tissue Sarcomas

Inclusion Criteria: 1. Must have histologically or cytologically confirmed diagnosis of locally advanced soft tissue sarcoma of extremity, trunk or retroperitoneum that is resectable and for which preoperative radiotherapy is considered appropriate. 1. Including metastatic (stage IV) disease for which radiotherapy and surgical resection of the primary tumor are indicated. 2. Grade 1 myxoid liposarcoma can be included if preoperative radiotherapy is considered appropriate. 3. For all other sarcomas, only grade 2 or 3 will be included. 2. Those with locally recurrent sarcoma after surgery alone are eligible for enrollment if other inclusion criteria are met. 3. Must have measurable disease defined as a tumor size at least \>= 5 cm in the longest diameter as measured by Computerized tomography (CT) scan or Magnetic resonance imaging (MRI) for which radiation is feasible and indicated. 4. Age \>=18 years. 5. Eastern Cooperative Oncology Group (ECOG) performance status \<= 1 (Karnofsky ≥ 70%). 6. Demonstrates adequate organ function within 21 days of Day 1 as defined below: 1. Hemoglobin \>= 9.0 g / dL. 2. prothrombin time (PT) (or International Normalized Ratio (INR)) and partial thromboplastin time (PTT) (or activated partial thromboplastin time (aPTT)) \<1.5 x upper limit of normal (ULN). 3. Absolute neutrophil count \>=1,500/microliter (mcL). 4. Platelets \>=100,000/mcL. 5. Total bilirubin within normal institutional limits, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits. 6. Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT)\<=3 X institutional upper limit of normal. 7. Alanine aminotransferase (ALT)/serum glutamic-pyruvic transaminase (SGPT) \<=3 X institutional upper limit of normal. 8. Alkaline phosphatase (ALP) \< 2.5 × ULN. 9. Creatinine \<= 2 x within institutional upper limit of normal OR creatinine clearance Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2, calculated using the Cockcroft-Gault equation, unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2. 7. Ability to understand and the willingness to sign a written informed consent document. 8. Human immunodeficiency virus (HIV)-infected individuals on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. 9. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. 10. Individuals with a history of hepatitis C virus (HCV) infection must have been treated and cured. For individuals with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. 11. Individuals with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. 12. The effects of Lurbinectedin on the developing human fetus are unknown. For this reason and because Lurbinectedin used in this trial are known to be teratogenic, women of childbearing potential and men must agree to use adequate contraception (2 methods of contraception including hormonal and barrier method of birth control) for the duration of study participation and for 6 months after last administration of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. A female is considered to be of childbearing potential (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) if she meets the following criteria: * is postmenarchal, * has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and * has not undergone surgical sterilization (removal of ovaries and/or uterus). - Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after last administration of study treatment. Exclusion Criteria: 1. Has the following histologic subtypes: gastrointestinal stromal tumor (GIST), desmoid, Ewing sarcoma, bone sarcomas, Kaposi sarcoma. 2. Prior history of trabectedin or lurbinectedin treatment. 3. Prior radiation therapy in excess of 20 Gray (Gy) conventionally fractionated radiotherapy (RT) to the site of the current diagnosis of sarcoma. No overlap with prior radiation fields in excess of 20 Gy is allowed. 4. Currently receiving treatment in another invasive investigational device or drug study, or less than 30 days since ending treatment on another investigational device or drug study(s). 5. Known central nervous system (CNS) disease, except for treated brain metastasis: Treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing requirement for dexamethasone, as ascertained by clinical examination and brain imaging (MRI or CT) during the screening period. Anticonvulsants (stable dose) are allowed. Treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS); Gamma Knife, linear particle accelerator (LINAC), or equivalent) or a combination as deemed appropriate by the treating physician. Participants with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to Day 1 will be excluded. 6. History of allergic reactions attributed to compounds of similar chemical or biologic composition to lurbinectedin. 7. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 8. Participants on strong or moderate cytochrome P450 (CYP)3A inducers or inhibitors and cannot be substituted for other drugs. 9. Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this study. 10. Has received systemic anti-cancer therapies within 3 weeks of first dose, radiation within 2 weeks, or antibody therapy within 4 weeks. Concomitant administration of Luteinizing hormone-releasing hormone (LHRH) analogues for prostate cancer and somatostatin analogues for neuroendocrine tumors are allowed as per standard of care. 11. Has not recovered from adverse events due to prior anti-cancer therapy to \<= grade 1 or baseline (other than alopecia). 12. Is currently receiving any other investigational agents. 13. Any concurrent illness in the opinion of the investigator would affect treatment compliance. 14. Participants needing concurrent antiemetic aprepitant or any other Neurokinin 1 (NK1) antagonist or related Substance P-antagonists (except rolapitant). 15. Pregnant participants are excluded from this study because lurbinectedin has the potential for teratogenic or abortifacient effects. Females of childbearing potential (definition as above) must undergo a urine pregnancy test per institutional guidelines within 7 days prior to Day 1 of study treatment. Participants with a positive urine pregnancy test are excluded. 16. Breast-feeding participants are excluded from this study because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lurbinectedin, breastfeeding should be discontinued if the mother is treated with lurbinectedin and for 2 weeks after the last dose. 17. Participants of childbearing potential who are unwilling to use at least 2 highly effective methods of contraception during study treatment and for 90 days following the last dose of study treatment. 18. Participants with a known history of collagen vascular disease on active therapy.