Brief Summary: This phase I trial tests the safety, side effects, and best dose of combination therapy with pelcitoclax (APG-1252) and cobimetinib in treating patients with ovarian and endometrial cancers that have come back after a period of improvement (recurrent). APG-1252 is a drug that inhibits activity of proteins that prevent cell death, leading to increased cell death and reduced cell growth. Cobimetinib is used in patients whose cancer has a mutated (changed) form of a gene called BRAF. It is in a class of medications called kinase inhibitors. It works by blocking the action of an abnormal protein that signals cancer cells to multiply. This helps slow or stop the spread of cancer cells. Giving APG-1252 in combination with cobimetinib may shrink or stabilize tumor in patients with recurrent ovarian and endometrial cancers.

Detailed Description: PRIMARY OBJECTIVE: I. To establish the recommended phase 2 dosing (RP2D) for combination pelcitoclax (APG-1252) and cobimetinib in advanced/recurrent endometrial and ovarian cancers. SECONDARY OBJECTIVES: I. To observe and record anti-tumor activity. II. To assess the side effects associated with combination APG-1252 and cobimetinib in advanced/recurrent endometrial and ovarian cancers, as measured by treatment-emergent and treatment-related adverse events by Common Terminology Criteria for Adverse Events (CTCAE) criteria. III. To assess the activity of combination APG-1252 and cobimetinib in advanced/recurrent endometrial and ovarian cancers, via measures of clinical activity, including response rate (RR), progression-free survival (PFS), clinical benefit rate (CBR), and duration of response (DoR). TRANSLATIONAL OBJECTIVES: I. To evaluate the pharmacodynamic effects of combination APG-1252 and cobimetinib on BCL-xL activity, including BCL-xL:BAX and BCL-xL-BAK heterodimers, as measured by the National Clinical Laboratory Network (NCLN) apoptosis multiplex immunoassay. II. To evaluate markers of response and resistance to APG-1252 and cobimetinib via whole exome sequencing and ribonucleic acid (RNA) sequencing obtained in pre-treatment/archival and on-treatment samples. III. To explore the effect of combination APG-1252 and cobimetinib on RAS pathway signaling, as measured by the NCLN ERK/MEK multiple immunoassay, and the association between RAS pathway activation with activity of combination APG-1252 and cobimetinib. IV. To explore markers of response and resistance to APG-1252 and cobimetinib through evaluation of BIM and MCL1 expression and RAS pathway signaling by reverse phase protein array (RPPA) and by BIM and pERK expression by immunohistochemistry. V. To determine pharmacokinetic (PK) parameters of APG-1252 and cobimetinib in combination. VI. To investigate RAS allelic burden and resistance mutations in patients receiving combination APG-1252 and cobimetinib. OUTLINE: This is a dose-escalation study of APG-1252 and cobimetinib followed by a dose-expansion study. Patients receive APG-1252 intravenously (IV) once a week (Q7D). Patients also receive cobimetinib orally (PO) once a day (QD) on days 1-21 of each cycle. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients also undergo biopsy and collection of blood on study and undergo computed tomography (CT) and/or magnetic resonance (MRI) throughout the trial. Patients undergo echocardiography (ECHO) or multigated acquisition scan (MUGA) during screening and on study. Patients are followed for up to 30 days after removal from study therapy.