The maximum tolerated dose (MTD) of E7389 liposomal formulation (E7389-LF) will be determined in the dose escalation part. Safety, pharmacokinetics (PK) and efficacy will be assessed using treatment regimen evaluated in dose escalation part in participants with breast cancer (up to 3 prior regimens of chemotherapy) in the expansion part 1 and in participants with adenoid cystic carcinoma (ACC), gastric cancer (GC), esophageal cancer (EGC), small cell lung cancer (SCLC) and breast cancer (with no prior regimens of chemotherapy) in the expansion part 2, 3, 4, 5 and 6 respectively.

Inclusion Criteria:

• Participants with advanced, nonresectable, or recurrent solid tumor for which no alternative standard therapy or no effective therapy exists
• Expansion-part 1 only: breast cancer with confirmed diagnosis, human epidermal growth factor (HER2) negative (immunohistochemistry [IHC] 0/1+, or fluorescence in situ hybridization [FISH] negative), prior chemotherapy of anthracycline and taxane (unless contraindicated), and up to 3 prior chemotherapy regimens to advanced or metastatic disease Expansion-part 2 only: nonresectable ACC with confirmed diagnosis and one or more prior chemotherapy regimens (unless contraindicated) Expansion-part 3, 4 and 5 only: nonresectable GC, EGC and SCLC with confirmed diagnosis and 2 or more prior chemotherapy regimens (unless contraindicated) (1 or more prior chemotherapy regimens for EGC participant who received combination therapy of platinum and taxane).

Ex-part 6 only: breast cancer with confirmed diagnosis, HER2 negative (IHC 0/1+, or FISH negative) and without prior chemotherapy regimens to advanced or metastatic disease. Participants with triple-negative breast cancer (TNBC) who are PD-L1 negative as assessed by the site or who are medically determined by the investigator(s) to be ineligible for treatment with atezolizumab and other immune-checkpoint inhibitors will be included.

• Life expectancy of greater than or equal to (>=) 12 weeks

• Eastern Cooperative Oncology Group-Performance Status (ECOG-PS) of 0 to 1

• Japanese participants aged >=20 years at the time of informed consent

• All adverse events (AEs) due to previous anti-cancer therapy have either returned to Grade 0 or 1 except for alopecia and Grade 2 peripheral neuropathy

• Adequate washout period before study drug administration:

  • Chemotherapy, hormonal therapy and radiotherapy: 3 weeks or more
  • Any therapy with antibody: 4 weeks or more
  • Any investigational drug or device: 4 weeks or more
  • Blood/platelet transfusion or granulocyte-colony stimulating factor (G-CSF): 2 weeks or more

• Adequate renal function defined as serum creatinine less than (<) 2.0 milligrams per deciliter (mg/dL) or creatinine clearance >=40 milliliters per minute (mL/min) per the Cockcroft and Gault formula

• Adequate bone marrow function:

  • Absolute neutrophil count (ANC) >=2,000/millimeters cubed (mm^3) (>=2.0 × 10^3/microliter [µl])
  • Platelets >=100,000/mm^3 (>=100 × 10^9/Liter [L])
  • Hemoglobin >=9.0 grams (g)/dL (Expansion-part only: >=8.5 g/dL)

• Adequate liver function:

  • Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) less than or equal to (<=) 1.5
  • Total bilirubin <=1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome
  • Alkaline phosphatase, alanine aminotransferase (ALT), and aspartate aminotransferase (AST) <=3 × ULN (<=5.0 times ULN in the participants with liver metastases)

• Expansion-part only: At least one measurable lesion based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1

• Willing and able to give informed consent and comply with all aspects of the protocol

Exclusion Criteria:

• Any of cardiac conditions as follows:

  • Heart failure New York Heart Association (NYHA) Class II or above
  • Unstable ischaemic heart disease (myocardial infarction within 6 months prior to starting study drug, or angina requiring use of nitrates more than once weekly)
  • Prolongation of Fridericia's corrected QT (QTcF) interval to greater than (>) 480 milliseconds (msec)

• History of hypersensitivity reaction by liposomal formulation agent

• Major surgery within 21 days prior to starting study drug

• Previous treatment with eribulin

• Previous radiation therapy encompassing an extensive region including the bone marrow (example, >30% of bone marrow)

• Known intolerance to the study drug or any of the excipients

• Known to be human immunodeficiency virus (HIV) positive

• Active viral hepatitis (B or C) as demonstrated by positive serology or requiring treatment

• Diagnosed with meningeal carcinomatosis

• Participants with brain or subdural metastases or invasion are not eligible, unless they have completed local therapy and have discontinued the use of corticosteroids for this indication for at least 4 weeks before starting treatment in this study. Any signs (example, radiologic) or symptoms of brain metastases must be stable for at least 4 weeks before starting study treatment.

• Pulmonary lymphangitic involvement that results in pulmonary dysfunction requiring active treatment, including the use of oxygen.

• Expansion-part only: history of active malignancy (except for primary tumor, or definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, carcinoma in-situ of the bladder or cervix, or early stage gastric/colorectal cancer) within the past 24 months prior to the first dose of study drug

• Evidence of clinically significant disease/status (example, cardiac, respiratory, gastrointestinal, renal disease) that in the opinion of the investigator(s) could affect the participant's safety or interfere with the study assessments

• Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin [β-hCG] or hCG test). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first dose of study drug.

• Males with impregnate potential or females of childbearing potential who or whose partner do not agree with medically effective method of contraception throughout the entire study period and for 28 days (90 days for male) after study drug discontinuation

• Ex-part 6 only: Active or acute oral infection requiring dental treatment

• Ex-part 6 only: Participants who received taxanes as neoadjuvant or adjuvant chemotherapy and have radiographically progressive disease by investigator(s) decision within 12 months after the last dose of taxane

• Ex-part 6 only: Child-Pugh score B or C