Participants with triple negative phenotype: estrogen receptor, progesterone receptor and human estrogen receptor-2 (HER-2) negative status for breast cancer (abnormal tissue that grows and spreads in the body until it kills) will receive trabectedin 1.3 milligram per meter square (mg/m^2) intravenous infusion (a fluid or a medicine delivered into a vein by way of a needle) over 3-hours (hrs) 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. Along with study drug participants will be given dexamethasone 4 milligram (mg) orally 24 hrs and 12hrs before study drug infusion on Day -1, followed by dexamethasone 20 mg intravenously 30 minutes before study drug infusion on Day 1, followed by dexamethasone 4 mg orally 24, 36, 48, 60 and 72hrs after the start of study drug infusion from Day 1 to 3.

Participants with overexpressing HER-2 breast cancer will receive trabectedin 1.3 mg/m^2 intravenous infusion over 3-hrs 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. Along with study drug participants will be given dexamethasone 4 milligram (mg) orally 24 hrs and 12hrs before study drug infusion on Day -1, followed by dexamethasone 20 mg intravenously 30 minutes before study drug infusion on Day 1, followed by dexamethasone 4 mg orally 24, 36, 48, 60 and 72 hrs after the start of study drug infusion from Day 1 to 3.

Participants with familial breast cancer gene 1 (BRCA1) or breast cancer gene 2 (BRCA2) mutation carriers cancer will receive trabectedin 1.3 mg/m^2 intravenous infusion over 3-hrs 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. Along with study drug participants will be given dexamethasone 4 mg orally 24 hrs and 12hrs before study drug infusion on Day -1, followed by dexamethasone 20 mg intravenously 30 minutes before study drug infusion on Day 1, followed by dexamethasone 4 mg orally 24, 36, 48, 60 and 72 hrs after the start of study drug infusion from Day 1 to 3.

Dexamethasone 4 mg orally 24 hrs and 12 hrs before study drug infusion on Day -1, followed by dexamethasone 20 mg intravenously 30 minutes before study drug infusion on Day 1, followed by dexamethasone 4 mg orally 24, 36, 48, 60 and 72 hrs after the start of study drug infusion on Day 1 to 3.

Percentage of participants with confirmed objective response will be based on assessment of confirmed complete response (CR) or confirmed partial response (PR) according to Response Evaluation Criteria in Solid Tumors (RECIST). Confirmed responses are those that persist on repeat imaging study at least 4 weeks after initial documentation of response. CR is defined as disappearance of all target lesions. PR is those with at least 30 percent decrease in the sum of longest dimensions of target lesions taking as a reference baseline sum longest dimensions. IER will be done to re-examine all Investigator assessed outcomes.

Percentage of participants with objective response based assessment of confirmed CR or confirmed PR according to RECIST. Confirmed responses are those that persist on repeat imaging study at least 4 weeks after initial documentation of response. The CR is defined as disappearance of all target lesions. The PR is those with at least 30 percent decrease in the sum of longest dimensions of target lesions taking as a reference baseline sum longest dimensions.

Duration of Response is considered as time in months from the first documentation of objective tumor response to objective tumor progression or death due to any cause. Duration of tumor response was calculated as: (the date of the first documentation of objective tumor progression or death due to cancer minus the date of the first CR or PR that will be subsequently confirmed plus 1) divided by 30.44. DR will be calculated for the subgroup of participants with a confirmed objective tumor response. IER will be done to re-examine all Investigator assessed outcomes and to provide an independent assessment of response and progression date.

An adverse event is any untoward medical event that occurs in a participant administered an investigational product, and it does not necessarily indicate only events with clear causal relationship with the relevant investigational product.