Birinapant and Carboplatin in Treating Patients and Targeting Recurrent High Grade Ovarian, Fallopian Tube, or Primary Peritoneal Cancer (HGSOC)

Inclusion Criteria: * All patients must have measurable disease by imaging defined as tumor that can be measured \>= 10 mm with multiparametric magnetic resonance imaging (MRI) (primary modality of imaging) or computed tomography (CT) (as an alternative) or \>= 10 mm by caliper on physical examination * Participant is capable of understanding and complying with parameters as outlined in the protocol and able to sign and date the informed consent, approved by an Independent Ethics Committee (IEC)/Institutional Review Board (IRB), prior to initiation of any screening or study-specific procedures * The participant must have a histologic diagnosis of recurrent high grade serous ovarian cancer (ovarian, tubal, peritoneal), to be treated with chemotherapy * Participants must have an image guided biopsy performed to yield fresh tissue for the in vitro organoid bio-assay and two biomarker testing (western blot and immunohistochemistry) * Only patients with tumors that score positive in the in vitro organoid bio-assay will be enrolled in the clinical trial; patients with tumors that score negative in this bio-assay will be considered screening failures and will not be enrolled in the clinical trial * Participant must have either no neuropathy (sensory and motor) or neuropathy less than or equal to grade 1 * The participant must have an Eastern Cooperative Oncology Group (ECOG) score between 0 - 2 at screening * The participant must have a life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1,500/mm\^3 * Platelets \>= 100,000/ mm\^3 * Hemoglobin \>= 9 g/dL or equivalent * Total bilirubin =\< 1.5 ? institutional upper limit of normal (ULN), unless known Gilbert?s syndrome has been diagnosed * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 ? institutional ULN (=\< 5 ? ULN if liver metastasis) * Serum creatinine =\< 1.5 ? ULN or creatinine clearance \>= 50 mL/min/1.73 m\^2 * Amylase \< ULN * Lipase \< ULN * Female participants of childbearing potential must have a negative serum pregnancy test at screening and negative (serum or urine) pregnancy test within 72 hours before the first study-drug dose; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required; the serum pregnancy test must be negative for the participant to be eligible * Female participants of childbearing potential should ensure use of a highly effective method of birth control as defined by the investigator, for example, those which result in a low failure rate (i.e., less than 1% per year) when used consistently and correctly such as implants, injectable, combined oral contraceptives, some intrauterine devices (IUDs), sexual abstinence or vasectomized partner during the study and for a period of at least 4 months following the last dose of any drug administered during the study Exclusion Criteria: * Patients with tumors that score negative in the in vitro organoid bio-assay will be excluded * Patients with non-measurable disease \< 10 mm on multiparametric MRI or CT scan will be excluded * Participants with a secondary malignancy that is progressing or requires active treatment; participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or in situ cervical cancer that has undergone potentially curative treatment are not excluded * Participants who have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to birinapant or its constituents * Participants requiring the use of anti-tumor necrosis factor (anti-TNF) therapies, such as infliximab, or has received treatment with anti-TNF therapies within 5 half-lives of the drug * Participants with an uncontrolled inter-current illness including, but not limited to, symptomatic congestive heart failure, hypertension, unstable angina pectoris, cardiac arrhythmia, autoimmune disease or inflammatory diseases, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women or women who expect to conceive a child are excluded from the study; breastfeeding should be discontinued if the mother is treated on this study * Participants who have a known active infection requiring systemic therapy, including human immunodeficiency virus (HIV), hepatitis B, and hepatitis C * Participants with a history of cranial nerve palsy * Participant is or has an immediate family member (e.g., spouse, parent/legal guardian, sibling or child) who is an investigational site or sponsor-investigator staff directly involved with this trial, unless prospective IRB approval (by chair or designee) is granted allowing exception to this criterion for a specific subject * In the opinion of the investigator, the participant is an unsuitable candidate for this study * Patients who are taking or anticipate taking any maintenance therapy while actively being treated on protocol or while being followed on protocol will be excluded; an example of this would be maintenance therapy with a Poly (adenosine diphosphate \[ADP\]-ribose) polymerase (PARP) inhibitor such as olaparib