Randomized Trial in Advanced, Metastatic or Unresectable Soft Tissue Sarcoma After Failure of Standard Treatments.

Inclusion Criteria: * Provision of written informed consent prior to any study specific procedures. * Patients with histologically documented and not surgically resectable or metastatic STS that progressed after first- or further-line treatments for relapsing disease. * At least one previous line of anthracycline-containing chemotherapy for advanced disease or relapsed/progressed within six months of a previous treatment with an anthracycline-containing chemotherapy in the neo-adjuvant/adjuvant setting. * Central revision will be mandatory in order to enroll a patient. Central revision will assess both diagnosis and adequacy of tumor specimen (minimum requisite will be a formalin-fixed paraffin-embedded block of either a 16-gauge tru-cut biopsy or a non-necrotic surgical tumor specimen). The patient has to consent BReast CAncer genes 1 and 2 (BRCA1 and BRCA 2) evaluation in the interest of avoiding misleading interpretation of resulting data. * Measurable disease according Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. Patients with an ECOG 2 are eligible if it depends solely on orthopedic problems. * Estimated life expectancy of at least 16 weeks. * Age ≥18 years. * Left Ventricular Ejection Fraction ≥ 50% and/or above lower institutional limit of normality * Adequate bone marrow, liver and renal function assessed within 7 days prior to * Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1 Exclusion Criteria: * Previous enrolment in the present study * Participation in another clinical study with an investigational product during the last 4 weeks. * Previous treatment with trabectedin, olaparib or other Poly Adpribose polymerase 1 (PARP-1) inhibitors or analogue. * Persistent toxicities (≥ grade 2 according Common Terminology Criteria for Adverse Events - CTCAE) with the exception of alopecia, caused by previous anticancer therapies. * Dementia or significantly altered mental status (e.g., psychiatric disorder) that would prevent the understanding or rendering of informed consent and compliance with the requirements of this protocol. * Patients with any severe and/or uncontrolled medical conditions such as unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction ≤ 6 months, serious uncontrolled cardiac arrhythmia, uncontrolled hyperlipidemia, active or uncontrolled severe infection, cirrhosis, chronic or persistent active hepatitis or severely impaired lung function. In particular for history of cardiac disease: congestive heart failure \>New York Hearth Association (NYHA) class 2; active coronary artery disease (myocardial infarction more than 6 months prior to study entry is allowed); cardiac arrhythmias requiring anti-arrhythmic therapy (beta blockers or digoxin are permitted) or uncontrolled hypertension, unstable spinal cord compression (untreated and unstable for at least 28 days prior to study entry), superior vena cava syndrome, extensive bilateral lung disease. * Immunocompromised patients, e.g., patients who are known to be serologically positive for Human Immunodeficiency Virus (HIV). * Active clinically serious infections (\> grade 2 CTCAE). * Active viral hepatitis \[Hepatitis B Virus - (HBV) or Hepatitis C Virus (HCV) infection\] * Metastatic brain or meningeal tumors (unless the patient is \> 6 months from definitive therapy, does not require corticosteroid treatment, has a negative imaging study within 4 weeks of study entry and is clinically stable with respect to the tumor at the time of study entry). Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days. * Patients with seizure disorders requiring medication (such as steroids or anti-epileptics). * Pregnant or breast-feeding patients. Women of childbearing potential must have a negative pregnancy test performed within 28 days before the start of treatment. Pregnancy test will be repeated and confirmed on cycle 1 day 1 before treatment start. Both men and women enrolled in this trial must use adequate barrier birth control measures during the course of the trial and 5 months after last dose of study drug. * Patients with evidence or history of bleeding diathesis. * Patients undergoing renal dialysis. * Patients unable to swallow oral medications. * Uncontrolled diabetes (fasting glucose \> 2 x Upper Normal Limit). * Patients receiving chronic, systemic treatment with corticosteroids or another immunosuppressive agent (except corticosteroids with a daily dosage equivalent to prednisone ≤ 20 mg for adrenal insufficiency). Topical or inhaled corticosteroids are permitted. * Other malignancy unless curatively treated with no evidence of disease for ≥5 years except: adequately treated non-melanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ , Stage 1, grade 1 endometrial carcinoma. Patients with a history of localised triple negative breast cancer may be eligible, provided they completed their adjuvant chemotherapy more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease * Patients with severe and/or uncontrolled concurrent medical disease that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol (e.g. impairment of gastrointestinal (GI) function, or GI disease that may significantly alter the absorption of the study drugs). * Anticancer chemotherapy or immunotherapy during the study or within 4 weeks of study entry * Radiotherapy during study or within 3 weeks of start of study drug. (Palliative radiotherapy will be allowed). * Major surgery within 4 weeks of start of study. Thus, patients must have recovered from wound or directly surgical related complications at time of study randomization. * Investigational drug therapy outside of this trial during or within 4 weeks of study entry. * Patients with known hypersensitivity to trabectedin, olaparib or to their excipients. * Patients can receive a stable dose of bisphosphonates for bone metastases before and during the study as long as these were started at least 4 weeks prior to treatment with the study drugs. * Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results. * A history of noncompliance to medical regimens or inability or unwillingness to return for scheduled visits. * Resting ElectroCardioGram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (eg., unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, corrected QT prolongation \>500 ms, electrolyte disturbances, etc.), or patients with congenital long QT syndrome. * Concomitant use of known strong CYtochromeP3A (CYP3A) inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting study drugs is 2 weeks. * Concomitant use of known strong (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort ) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting study drugs is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. * Previous allogenic bone marrow transplant or double umbilical cord blood transplantation * Patients with myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of them