Eribulin Mesylate in Treating Patients With Recurrent Ovarian Epithelial, Primary Peritoneal Cavity, or Fallopian Tube Cancer

Inclusion Criteria:

* Histologically or cytologically confirmed ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer

  * Recurrent disease after ≥ 1 prior therapy, meeting 1 of the following criteria:

    * Platinum-resistant disease (progression-free interval \< 6 months)
    * Platinum-sensitive disease (progression-free interval ≥ 6 months)
* Measurable disease, defined as ≥ 1 unidimensionally measurable lesion ≥ 20 mmby conventional techniques OR ≥ 10 mm by spiral CT scan
* No known brain metastasis
* Life expectancy \> 2 months
* ECOG performance status (PS) 0-1 OR Karnofsky PS 70-100%
* Absolute neutrophil count ≥ 1,500/mm³
* Platelet count ≥ 100,000/mm³
* WBC ≥ 3,000/mm\^3
* Bilirubin normal
* AST and ALT ≤ 2.5 times upper limit of normal
* Creatine normal OR creatinine clearance ≥ 60 mL/min
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* No prior invasive malignancy within the past 5 years except nonmelanoma skin cancer

  * Stage IA or IB endometrial cancer within the past 5 years allowed provided patient is considered disease free
* No history of allergic reaction attributed to compounds of similar chemical or biological composition to E7389
* No HIV positivity
* No ongoing or active infection
* No cardiac arrhythmia
* No unstable angina pectoris
* No symptomatic congestive heart failure
* No psychiatric illness or social situations that would preclude study compliance
* No other uncontrolled intercurrent illness
* See Disease Characteristics
* Recovered from effects of recent surgery, radiotherapy, or chemotherapy
* No more than 2 prior cytotoxic therapies with no more than 1 non platinum, non taxane regimen
* No prior E7389
* More than 14 days since prior hormonal therapy
* More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C)
* More than 4 weeks since prior radiotherapy
* No concurrent antitumor hormonal therapy
* No other concurrent investigational agents
* No other concurrent anticancer agents or therapies
* No granulocyte colony-stimulating factors during the first course of study therapy