• For dose escalation, patients must have histologically or cytologically confirmed recurrent epithelial ovarian, fallopian tube, or primary peritoneal cancer, or endometrial cancer that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective. For expansion, patients must have histologically or cytologically confirmed recurrent epithelial ovarian, fallopian tube, or primary peritoneal cancer

• Prior lines:

‣ Patients must have received at least one prior line of platinum-based systemic therapy. Platinum received together with radiation as a sensitizing agent is not considered a systemic line of therapy

⁃ Patients with low grade serous ovarian cancer must have received a prior MEK inhibitor at a demonstrated therapeutic dose (i.e., trametinib 1mg daily or higher; binimetinib 30mg twice daily or higher). Patients who have had prior cobimetinib must have been able to tolerate cobimetinib at the dose and schedule they would receive it on study

⁃ Patients with microsatellite instability (MSI) or mismatch repair deficient (dMMR) endometrial cancer must have received prior PD-1 or PD-L1 directed immunooncology (IO) therapy or be considered medically ineligible to receive such therapy

• Patients with ovarian cancer must have platinum-resistant disease (progression within 6 months of last receipt of platinum)

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of APG-1252 (pelcitoclax) in combination with cobimetinib in patients \< 18 years of age, children are excluded from this study

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

• Absolute neutrophil count \>= 1,500/mcL

• Platelets \>= 100,000/mcL

• Hemoglobin \> 9 g/dL

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) \< 3 x institutional ULN

• Creatinine =\< 1.5 x institutional ULN OR glomerular filtration rate (GFR) \>= 50 ml/min (based on the calculated Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) glomerular filtration rate estimation

• Left ventricular ejection fraction (LVEF) \>= institutional lower limit of normal (LLN) (or above 50%, whichever is higher) by echocardiogram (ECHO) or multigated acquisition scan (MUGA)

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy (that are not excluded) with undetectable viral load within 6 months are eligible for this trial

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression by scan and stable off systemic steroids for at least 4 weeks

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better

• Patients should be able to swallow oral therapy

• The effects of APG-1252 on the developing human fetus are unknown. For this reason and because other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and for 2 weeks after completion of APG-1252 and cobimetinib administration. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 2 weeks after completion of APG-1252 and cobimetinib administration

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity who have a legally-authorized representative (LAR) and/or family member available will also be eligible

• Patients must be willing to release archival tissue if available

• Patients on dose level 2 or higher in the escalation cohort and patients in the expansion cohort must have measurable and biopsiable disease (in a lesion that is not being utilized as a target lesion for Response Evaluation Criteria in Solid Tumors \[RECIST\] assessment)