Paclitaxel, Polyglutamate Paclitaxel, or Observation in Treating Patients With Stage III or Stage IV Ovarian Epithelial, Peritoneal Cancer, or Fallopian Tube Cancer

Inclusion Criteria:

* Patients with a histologic diagnosis of primary peritoneal carcinoma, or stage III or IV epithelial ovarian or fallopian tube carcinoma, with either optimal (=\< 1 cm residual disease) or suboptimal residual disease following initial surgery; all patients must have had appropriate surgery for ovarian, primary peritoneal or fallopian tube carcinoma with appropriate tissue available for histologic evaluation to confirm diagnosis and stage
* Patients with the following histologic epithelial cell types are eligible:

  * Serous adenocarcinoma
  * Endometrioid adenocarcinoma
  * Mucinous adenocarcinoma
  * Undifferentiated carcinoma
  * Clear cell adenocarcinoma
  * Mixed epithelial carcinoma
  * Transitional cell carcinoma
  * Malignant Brenner tumor
  * Adenocarcinoma not otherwise specified (NOS)
* Patients must have completed treatment within the past 12 weeks with at least 5 cycles and not more than 8 cycles of a platinum (IV or intraperitoneal \[IP\]) and paclitaxel or docetaxel-based combination chemotherapy and have no symptoms suggestive of persistent cancer, normal (no evidence of cancer) computed tomography (CT) scan of the abdomen/pelvis and normal cancer antigen 125 (CA-125) following this therapy

  * Patients treated with neo-adjuvant platinum-taxane chemotherapy for a presumptive diagnosis of stage III or IV epithelial ovarian, primary peritoneal or, fallopian tube (by paracentesis, percutaneous biopsy or open biopsy) are eligible provided that they have undergone interval abdominal surgery after at least one but no more than six cycles of standard chemotherapy; such surgery must meet the same criteria as for those undergoing up front surgery, including tissue diagnosis for confirmation of primary tumor site and stage III or IV disease; also, patients must have received at least two cycles after interval abdominal surgery
* Absolute neutrophil count \>= 1,500/ul, equivalent to Common Toxicity Criteria (CTCAE version \[v\]3.0) grade 1
* Platelet count \>= 100,000/ul
* Creatinine =\< 1.5 times institutional upper limit of normal (ULN), CTCAE v3.0 grade 1
* Bilirubin =\< 1.5 times ULN, (CTCAE v3.0 grade 1)
* Serum glutamic oxaloacetic transaminase (SGOT) =\< 2.5 times ULN (CTCAE v3.0 grade 1)
* Alkaline phosphatase =\< 2.5 times ULN (CTCAE v3.0 grade 1)
* Neuropathy (sensory and motor) less than or equal to CTCAE v3.0 grade 1
* Gynecologic Oncology Group (GOG) performance status of 0, 1, or 2
* Patients must have signed an approved informed consent and Health Insurance Portability and Accountability Act (HIPAA) authorization
* Patients must complete pre-entry assessments

Exclusion Criteria:

* Patients with a current diagnosis of epithelial ovarian or fallopian tube tumor of low malignant potential (LMP) (Borderline carcinomas) are not eligible; patients with a prior diagnosis of a low malignant potential tumor that was surgically resected and who subsequently develop invasive adenocarcinoma are eligible, provided that they have not received prior chemotherapy for their ovarian LMP tumor
* Germ cell tumors, sex cord-stromal tumors, carcinosarcomas, mixed mullerian tumors or carcinosarcomas, metastatic carcinomas from other sites to the ovary and low malignant potential tumors including so called micropapillary serous carcinomas are not eligible
* Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis are excluded; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than 3 years prior to registration, and the patient remains free of recurrent or metastatic disease
* Patients who have received investigational therapies, and/or biological therapies (i.e. Bevacizumab or Erlotinib) for their epithelial ovarian, primary peritoneal or fallopian tube cancers or for any other abdominal or pelvic tumor, are not excluded; however, biologics cannot be continued concurrent with the GOG-012 maintenance treatment (or observation); patients who have received prior chemotherapy for any other abdominal or pelvic tumor (except as noted above) are excluded; patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than 3 years prior to registration, and that the patient remains free of recurrent or metastatic disease
* Patients with synchronous primary endometrial cancer, or a past history of primary endometrial cancer, are excluded, unless all of the following conditions are met:

  * Stage not greater than I-B
  * Less than 3 mm invasion without vascular or lymphatic invasion
  * No poorly differentiated subtypes, including papillary serous, clear cell, or other Federation of Gynecology and Obstetrics (FIGO) Grade 3 lesions
* With the exception of non-melanoma skin cancer and other specific malignancies as noted above, patients with other invasive malignancies who had (or have) any evidence of the other cancer present within the last 5 years or whose previous cancer treatment contraindicates this protocol therapy are excluded
* Patients with acute hepatitis, or known chronic hepatitis
* Patients with an active infection that requires antibiotics
* Patients with ongoing gastrointestinal bleeding requiring blood product support
* Patients whose circumstances at the time of entry onto the protocol would not permit completion of study or required follow up
* Patients with unstable angina or those who have had a myocardial infarction within the past six months; patients with evidence of abnormal cardiac conduction (e.g. bundle branch block, heart block) are eligible if their disease has been stable for the past six months
* Patients are excluded who have had prior therapy with CT-2103
* Patients with active bleeding or an unexplained prothrombin time (PT) or partial thromboplastin time (PTT) \> institutional upper limit normal (ULN)
* Patients who are pregnant or nursing are excluded; patients who may become pregnant must practice an effective method of birth control