Intraperitoneal Bortezomib and Carboplatin in Treating Patients With Persistent or Recurrent Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients must have recurrent or persistent epithelial ovarian, fallopian tube, or primary peritoneal cancer; histologic documentation of the original primary tumor is required via the pathology report * 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's tumor, or adenocarcinoma not otherwise specified (N.O.S) * Patients must have either measurable disease or detectable disease: * Measurable disease will be defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; measureable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Detectable disease is defined in a patient as one who does not have measurable disease but has at least one of the following conditions: * Baseline values of cancer antigen (CA)-125 at least twice the upper limit of normal * Ascites and/or pleural effusion attributed to tumor * Solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definitions for target lesions * In addition, patients are allowed to undergo surgical cytoreduction of relapsed disease as proof of detectable disease at the discretion of their treating physician; if performed to allow participation in this protocol, the operative and pathology reports will be required for submission * Patients must have a Gynecologic Oncology Group (GOG) performance status 0, 1, or 2 * Recovery from effects of recent surgery, radiotherapy, or chemotherapy * Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]) * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration; continuation of hormone replacement therapy is permitted * Any other prior therapy directed at the malignant tumor, including biological and immunologic agents, must be discontinued at least three weeks prior to registration * Patients must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound; this initial treatment may have included non-cytotoxic therapy, intraperitoneal therapy, consolidation, or extended therapy administered after surgical or non-surgical assessment * Patients are required to receive, one additional cytotoxic regimen for management of recurrent or persistent disease * Patients are allowed to receive, but are not required to receive, two additional cytotoxic regimens for management of recurrent or persistent disease (maximum number of prior cytotoxic regimens including primary therapy is 4); patients are allowed to receive, but are not required to receive, biologic (non-cytotoxic) therapy either alone or as part of the cytotoxic regimens for management of recurrent or persistent disease * Absolute neutrophil count (ANC) greater than or equal to 1,500/mcl, equivalent to the National Cancer Institute (NCI) Common Terminology Criteria (CTCAE) version 4 grade 1 * Platelets greater than or equal to 100,000/mcl * Creatinine less than or equal to institutional upper limit of normal (ULN) * Bilirubin less than or equal to 1.5 x ULN (per the NCI CTCAE version 4 grade 1) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) less than or equal to 3 x ULN (per the active version of the NCI CTCAE grade 1) * Alkaline phosphatase less than or equal to 2.5 x ULN (per the NCI CTCAE version 4 grade 1) * Neuropathy (sensory and motor) less than or equal to the NCI CTCAE version 4 grade 1 * Prothrombin time (PT) such that international normalized ratio (INR) is =\< 1.5 x ULN (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) * Partial thromboplastin time (PTT) =\< 1.5 x ULN (heparin, low molecular weight heparin, or alternative anticoagulants are acceptable) * Patients who have met the pre-entry requirements * An approved informed consent and authorization permitting release of personal health information must be signed by the patient or guardian * Patients of childbearing potential must have a negative serum pregnancy test prior to the study entry and be practicing an effective form of contraception * Patients in this trial may receive ovarian estrogen +/- progestin replacement therapy as indicated at the lowest effective dose(s) for control of menopausal symptoms at any time, but not progestins for management of anorexia while on protocol directed therapy or prior to disease progression Exclusion Criteria: * Patients who have had prior therapy with bortezomib * Patient with a history of other invasive malignancies, with the exceptions of non-melanoma skin cancer and localized breast cancer, are excluded if there is any evidence of other malignancy being present within the last five years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of ovarian cancer are excluded; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients who have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of ovarian cancer are excluded * Patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease * Patients with known brain metastases are excluded * History of allergic reactions attributed to carboplatin or compounds of similar chemical or biologic composition to bortezomib including boron or mannitol * 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; no more than superficial myometrial invasion, without vascular or lymphatic invasion; no poorly differentiated subtypes, including papillary serous, clear cell or other International Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions * Patients with a history of prior myocardial infarction in the last 12 months or patients with new electrocardiographic evidence of acute ischemia or new conduction abnormalities are ineligible * Uncontrolled concurrent illness including but not limited to ongoing or active infection that requires parenteral antibiotics, acute hepatitis, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with insulin-dependent diabetes will be excluded * Concomitant medications known to inhibit or induce cytochrome P450, family 3, subfamily A, polypeptide 4 (3A4) are to be avoided