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