This is an open-label (all people know the identity of the intervention), prospective (study following participants forward in time), multi-center (when more than 1 hospital or medical school team work on a medical research study) study evaluating the effectiveness and safety of trabectedin in 3 subpopulations of breast cancer participants: Group A: triple negative profile for estrogen receptor, progesterone receptor and human estrogen receptor, Group B: human epidermal growth factor receptor-2 overexpressing tumors (HER-2+) and Group C: familial breast cancer gene 1 (BRCA1) or breast cancer gene 2 (BRCA2) mutation carrier. Participants will receive trabectedin 1.3 milligram per square meter (mg/m\^2) intravenous infusion (a fluid or a medicine delivered into a vein by way of a needle) over 3-hour every 3 weeks, on Day 1 of each cycle. Each cycle length will be 3 weeks. Treatment will be continued until disease progression, unmanageable toxicity, participant refusal or treatment delay no longer than 3 weeks due to toxicity. Efficacy will be primarily evaluated by percentage of participants with confirmed objective response by independent external review and Investigators assessment. Participants' safety will be monitored throughout the study.
