Auranofin in Treating Patients With Recurrent Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Histological or cytological confirmation of epithelial ovarian, primary peritoneal, or fallopian cancer from any previous time point * Completion of initial therapy of epithelial ovarian, primary peritoneal, or fallopian cancer from any previous time point (includes completion of surgery and/or followed by post-operative chemotherapy including maintenance) with no subsequent treatment for progressive disease * An increase in serum CA 125 level, as defined as follows: 1) normalization of the CA 125 during first-line chemotherapy followed by an increase of \>= 100 units/mL; OR 2) normalization of the CA 125 during first-line chemotherapy followed by a doubling of the CA 125 beyond the upper limit of normal with a confirmatory measurement within a period of 4 weeks or less that shows the same or higher CA 125 level * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2 * Absolute neutrophil count (ANC) \>= 1500 * Platelets (PLT) \>= 100,000 * Hemoglobin (HgB) \> 9.0 g/dL * Bilirubin \< 1.5 x upper limit of normal (ULN) * Creatinine within institutional normal limits * Negative urine pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Willingness to be interviewed by telephone about CA 125 elevation * Able to provide informed written consent * Willing to provide tissue blocks for correlative research purposes (please note that if tissue blocks are unavailable, the patient will still be eligible provided they meet all other eligibility criteria) Exclusion Criteria: * Co-morbid systemic illnesses or other severe concurrent disease, which in the judgment of the treating oncologist, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Symptoms (other than anxiety, depression, or other psychological symptoms) that, in the opinion, of the treating oncologist are a direct result of cancer recurrence; (examples of symptoms that would preclude enrollment include unintentional weight loss and new abdominal pain) * Receiving any other prescribed therapy treatment for ovarian cancer * Any of the following because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects: * Pregnant women * Nursing women * Women of childbearing potential who are unwilling to employ adequate contraception