A Study of MORAb-202 (Herein Referred to as Farletuzumab Ecteribulin) in Participants With Solid Tumors

Inclusion Criteria: * Participants who have provided voluntary written consent for participation in this clinical study. * Participants to whom the rules for complying with this clinical study have been adequately explained, and who intend to and can comply with those rules. * Male or female participants age \>=20 years at the time of informed consent of screening 1 (or screening 2, in case of participants who enter this clinical study from screening 2). * Part 1 only: Participants with FRA-positive solid tumor confirmed by immunohistochemistry (IHC) assay at the central laboratory using their available tumor samples from resected specimen (i.e., surgical or excisional/incisional biopsy samples) or core needle biopsy (\<=18-gauge), or participants with a histological and/or cytological diagnosis of any serous ovarian carcinoma, fallopian tube carcinoma, endometrial carcinoma, or adenocarcinoma of Non-Small Cell Lung Cancer (NSCLC), whose archival resected tumor samples (that is, surgical or excisional/incisional biopsy sample). * Part 1 only: At informed consent of screening 2, participants who failed standard therapies, or for which no appropriate treatment is available. * Participants with adequate function of major organs within 2 weeks prior to the first administration of the study drug as follows. 1. Hemoglobin \>=9.0 grams per deciliter (g/dL). 2. Neutrophil count \>=1.5 × 10\^3/microliters (μL). 3. Platelet count \>=10 × 10\^4/μL. 4. Total bilirubin \<=1.5 × upper limit of normal (ULN) in the facility. 5. Alanine aminotransferase and aspartate aminotransferase \<=3.0 × ULN in the facility (in the case of liver metastases \<=5\*ULN). 6. Serum creatinine \<=1.5 × ULN in the facility. 7. Albumin \>=3 g/dL. * Participants with Performance Status score of 0-1 established by Eastern Cooperative Oncology Group. * Participants who are expected to survive for 3 months or longer after the first administration of the study drug. * Washout period required from the end of prior treatment to the first administration of the study drug will be as follows a. Anticancer therapy * Antibody and other study drugs: \>4 weeks (however, in the case where the half-life of other study drugs is known and 5 × half-lives of that study drug is less than or equal to 4 weeks, participants can be eligible after \>=5 × half-lives of that study drug has passed). * Prior chemotherapy (except small-molecule targeted therapy), surgical therapy, radiation therapy: \>3 weeks. * Endocrine therapy, immunotherapy except antibody, small-molecule targeted therapy: \>2 weeks. * Supportive therapies • Blood/platelet transfusion, hematopoietic stimulating agent including granulocyte colony-stimulating factor formulation: \> 2 weeks. * Participants whose formalin fixed, paraffin-embedded unstained slides of tumor sample are available for IHC test at central laboratory. If applicable biopsy will be performed by excisional, incisional or needle puncture (\<=18-gauge as far as possible). Inclusion Criteria (Part 2 only) * Measurable disease meeting the following criteria: 1. At least 1 lesion of \>=1.0 centimeters (cm) in the longest diameter for a non-lymph node or \>=1.5 cm in the short-axis diameter for a lymph node that is measurable according to Response Evaluation Criteria In Solid Tumors (RECIST) 1.1 using computerized tomography/magnetic resonance imaging. 2. Lesions that have had external beam radiotherapy or locoregional therapies such as radiofrequency ablation must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion. * Participants histologically diagnosed with the following ovarian carcinoma (including primary peritoneal carcinoma and fallopian tube carcinoma) or NSCLC. Participants for Cohort 1 and 3 who have archival resected tumor samples (that is, surgical or excisional/incisional biopsy sample) for IHC assay are not required to be FRA positive at the central laboratory (Screening 1 is not required). Participants for Cohort 1 and 3 who do not have archival resected tumor samples (that is, surgical or excisional/incisional biopsy sample) are required to be FRA positive at the central laboratory (Screening 1 is required). Participants for Cohort 2 and 4 are required to be FRA positive confirmed by IHC assay at the central laboratory using their available tumor samples from resected specimen (that is, surgical or excisional/incisional biopsy samples) or core needle biopsy (\<=18-gauge for ovarian carcinoma and for NSCLC \[adenocarcinoma and non-adenocarcinoma\] as possible) (Screening 1 is required). * Cohort 1: High grade serous adenocarcinoma * Cohort 2: Other histological types of ovarian carcinoma (excluding mucinous adenocarcinoma) * Cohort 3: NSCLC adenocarcinoma * Cohort 4: NSCLC non-adenocarcinoma * Participants with the following disease characteristics: 1. Ovarian carcinoma (including primary peritoneal carcinoma and fallopian tube carcinoma): * Participants with platinum-resistant disease (defined as progression radiographically within less than \[\<\] 6 months from completion of last platinum therapy) who have received \>4 cycles in last platinum-containing chemotherapy for ovarian carcinoma * Participants who have received up to two regimen of chemotherapy after diagnosed as platinum-resistant 2. NSCLC: * Participants that have advanced after previous treatment and those for which no alternative standard therapy exist and those who are not indicated for epidermal growth factor receptor (EGFR), BRAF V600E mutation, anaplastic lymphoma kinase (ALK) or reactive oxygen species (ROS)-targeted therapy (Participants who have progressed after prior such therapy may be eligible) Exclusion Criteria: * Medical history of clinically significant cardiovascular impairment: 1. Congestive heart failure greater than or equal to New York Heart Association Class III. 2. Unstable angina pectoris, myocardial infarction or stroke within 6 months before of the first administration of the study drug. 3. Prolongation of corrected QT (QTc) interval to \> 480 milliseconds (ms) (Fridericia method). 4. Arrhythmias associated with hemodynamic instability. * Concomitant systemic infection requiring medical treatment. * Participants who test positive for human immunodeficiency virus (HIV antibody). * Active viral hepatitis (B or C) (\*) as demonstrated by positive serology or requiring treatment. (\*) hepatitis B surface antigen (HBsAg), hepatitis B surface antibody (anti-HBs)/hepatitis B core antibody (HBcAb), and anti-hepatitis C virus (HCV) antibody test. Participants who are anti-HBs/HBcAb (+) without detectable hepatitis B virus (HBV)-deoxyribonucleic acid (DNA)/HCV- ribonucleic acid (RNA) are eligible. * Effusion requiring drainage continually. * Participants whose toxicity of previous treatment has not recovered to Grade 1 or lower (except for alopecia and hemoglobin). * Participants who have received a previous monoclonal antibody therapy and have evidence of an immune or allergic serious reaction. * Participants who had previous treatment with other folate receptor targeting agents. * Participants who have medical history of discontinuing prior eribulin due to toxicity. * Has an active pneumonitis/interstitial lung disease (ILD), a history of pneumonitis/ILD that required systemic steroids, received radiotherapy to lung field within 12 months before the first dose of study intervention, or current clinically relevant lung disease (example, Chronic Obstructive Pulmonary Disease). * Other active malignancy (except for definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix) within the past 24 months prior to the first administration of the study drug. * Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta-human chorionic gonadotropin or human chorionic gonadotropin). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 3 days before the first administration of the study drug (breastfeeding participants are not eligible even if they discontinue breastfeeding). * Women of childbearing potential or man of impregnate potential who don't agree that both the participant and his/her partner will use a medically effective method for contraception (as below) during the study and after study drug discontinuation (male; 90 days, female; 60 days). Note: Condom\*, contraceptive sponge\*\*, foam\*\*, jelly\*\*, diaphragm\*, intrauterine device\*, or use of oral contraception\* from at least 4 weeks before starting the study treatment (\*Approved drugs or certified medical devices in Japan, \*\*Non-approved drugs or certified medical devices in Japan). * Known intolerance to the study drug or any of the excipients. * Any medical or other condition that in the opinion of the investigator(s) would preclude the participant's participation in the study. * Scheduled for surgery during the study. * Diagnosed with meningeal carcinomatosis. * Participants with brain or subdural metastases 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 (e.g., radiologic) or symptoms of brain metastases must be stable for at least 4 weeks before starting study treatment. * Use of illegal recreational drugs. Exclusion Criteria (Part 2 only) * Previous treatment with eribulin * Participants histologically diagnosed with mucinous ovarian carcinoma * (Ovarian carcinoma only) Participants who progressed during the preceding platinum-containing chemotherapy (for platinum refractory)