Inclusion Criteria

Diagnosis: Histologically confirmed rhabdomyosarcoma (RMS), non-rhabdomyosarcoma soft tissue sarcoma (NRSTS) (Grade 2 or 3), or Ewing sarcoma (EWS) which is relapsed or refractory (failed front line therapy)

Therapeutic options: Participant's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life.

Participants must have fully recovered from the acute toxic effects of all prior anticancer therapy and must meet the minimum duration from prior anticancer directed therapy prior to study drug administration. If, after the required time frame, the numerical eligibility criteria are met, eg, blood count criteria, the participant is considered to have recovered adequately:

Adequate renal function

Adequate liver function

Exclusion Criteria

Pregnant or breastfeeding

Females of childbearing potential who:

- Do not agree to use a highly effective method of contraception for the entire study period and for 6 months after study drug discontinuation, ie: - Total abstinence (if it is their preferred and usual lifestyle); - An intrauterine device (IUD) or intrauterine system (IUS); - A contraceptive implant; - An oral contraceptive (must be on a stable dose of the same oral hormonal contraceptive product for at least 4 weeks before dosing with study drug and for the duration of the study and for 6 months after study drug discontinuation);

or

- Do not have a vasectomized partner with confirmed azoospermia.

Males who have not had a successful vasectomy (confirmed azoospermia) or if they and their female partners do not meet the criteria above (ie, not of childbearing potential or practicing highly effective contraception throughout the study period or for 3 months after study drug discontinuation). No sperm donation is allowed during the study period or for 3 months after study drug discontinuation.

Concomitant medications:

- Corticosteroids: Participants receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for at least 7 days prior to study drug administration (except when indicated for Central Nervous System [CNS] metastases, then participants must not have received corticosteroids for at least 28 days)

- Anticancer Agents: participants who are currently receiving other anticancer agents

- Anti-GVHD agents Post-transplant: Participants who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant

- Strong CYP3A4 inducers/inhibitors

- Received prior therapy with eribulin mesylate

Any other malignancy that required treatment (except for non-melanoma skin cancer, or histologically confirmed complete excision of carcinoma in situ), within 2 years prior to study drug administration

Has hypersensitivity to eribulin or any of the excipients

Has a prior history of viral hepatitis (B or C) as demonstrated by positive serology (presence of antigens) or have an uncontrolled infection requiring treatment. Participants with a known prior history of hepatitis B or C may be eligible pending agreement with the sponsor.

Has > Grade 1 peripheral sensory neuropathy or > Grade 1 peripheral motor neuropathy graded according to the Modified ("Balis") Pediatric Scale of Peripheral Neuropathies

Has cardiac pathology

Has CNS Disease

Have had or are planning to have the following invasive procedures:

- Major surgical procedure or significant traumatic injury within 28 days prior to study drug administration

- Laparoscopic procedure or open biopsy within 7 days prior to study drug administration

- Central line placement or subcutaneous port placement is not considered major surgery but must be placed at least 2 days prior to study drug administration

- Core biopsy, including bone marrow biopsy, within 2 days prior to study drug administration

- Fine needle aspirate within 3 days prior to study drug administration

- Has any serious concomitant illness that in the opinion of the investigator(s) could affect the participant's safety or interfere with the study assessments

- Participants with known human immunodeficiency virus (HIV); due to lack of available safety data for eribulin therapy in HIV-infected participants