This is an open-label (all people know the identity of the intervention), prospective (study following participants forward in time), multicenter (when more than one hospital or medical school team work on a medical research study) study of trabectedin for the treatment of localized myxoid / round cell liposarcoma (MRCL). Trabectedin will be given at 1.5 milligram per meter square (mg/m^2) over a 24-hour intravenous (iv) infusion every 3 weeks for a minimum of 3 and a maximum of 6 cycles along with dexamethasone 20 mg iv which will be given within 30 minutes before start of each trabectedin iv infusion. Participants whose myxoid/round cell liposarcoma (MRCL) do not progress at the end of the neoadjuvant treatment will be followed every 6 weeks for disease progression or until 6 months post definitive surgery, in the absence of unacceptable toxicity and/or disease progression. Efficacy will be assessed by determining the pathologic Complete Response (pCR) rate assessed in the tumor surgical specimen by a central pathology review. Participants' safety will be monitored throughout the trial.