Testing the Addition of Anti-Cancer Drug, ZEN003694 (ZEN-3694) and PD-1 Inhibitor (Pembrolizumab), to Standard Chemotherapy (Nab-Paclitaxel) Treatment in Patients With Advanced Triple-Negative Breast Cancer

Inclusion Criteria: * Participants must have a histologically or cytologically confirmed diagnosis of TNBC based on standard criteria for the disease: * Estrogen receptor (ER) and progesterone receptor (PR) \< 10% by immunohistochemistry (IHC), and HER2-negative (per current American Society of Clinical Oncology \[ASCO\]/College of American Pathologists \[CAP\] guidelines) * If there is more than one histological result available, the most recent sample with ER, PR and HER2 results will be considered for inclusion * Patients who have not had ER, PR and HER2 testing and thus, ER, PR and HER2 status is unknown, are not eligible * Participants without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation * Participants must have disease that is unresectable locally advanced or metastatic * DOSE ESCALATION COHORT: Known PD-L1 status is not required prior to study enrollment. Central PD-L1 testing (on archival tumor tissue) will occur retrospectively * DOSE ESCALATION COHORT: Any number of prior lines of therapy are allowed in the metastatic setting. Prior immune checkpoint inhibitor allowed in any setting * DOSE ESCALATION COHORT: Evaluable or measurable disease per RECIST 1.1 criteria * DOSE EXPANSION COHORT: PD-L1 status must be negative. Standard local testing with any PD-L1 antibody that has been validated in a Clinical Laboratory Improvement Act (CLIA)- certified environment will be acceptable for including patients on trial. Primary or metastatic samples may be tested for PD-L1 status. Central confirmation will occur retrospectively. For patients in whom a baseline research tumor tissue biopsy is not performed (e.g. site of disease is not safely accessible), archival tissue should be provided for central confirmatory PD-L1 testing * DOSE EXPANSION COHORT: 0-1 prior lines of systemic therapy in the metastatic setting * DOSE EXPANSION COHORT: Participants must have measurable disease per RECIST 1.1 criteria * DOSE EXPANSION COHORT: Participants must have disease that is amenable to biopsy as judged by the treating investigator and must be willing to undergo pre- and on-treatment tumor biopsies, if safely accessible * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of ZEN003694 (ZEN-3694) in combination with nab-paclitaxel and pembrolizumab (MK-3475) 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 \>= 1,000/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (or =\< 2.0 x ULN in patients with documented Gilbert's Syndrome) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3.0 x institutional ULN or ≤ 5.0 x institutional ULN for participants with documented liver metastases * Serum or plasma creatinine =\< 1.5 x institutional ULN OR glomerular filtration rate (GFR) \>= 60 mL/min (based on the calculated chronic kidney disease epidemiology (CKD-EPI) glomerular filtration rate estimation * International normalized ratio (INR) or prothrombin time (PT): =\< 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT): =\< 1.5 × ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial as long as their anti-retroviral therapy does not have the potential for drug-drug interactions as judged by the treating investigator * 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 history of treated central nervous system (CNS) metastases are eligible, provided they meet the following criteria: * Disease outside the CNS is present * Recovery from acute toxicity associated with the treatment to =\< Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 grade 1 or baseline (with the exception of alopecia), with no requirement for escalating doses of corticosteroids over the past 7 days * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy * 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 basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy, or in situ cervical cancer are allowed * Patients should be New York Heart Association Functional Classification of class 2B or better * Peripheral neuropathy grade =\< 1 * Ability to swallow and retain oral medications * Participants may not have had cytotoxic chemotherapy, immunotherapy, major surgery (other than diagnostic surgery, dental surgery or stenting), or other investigational therapy within 3 weeks prior to entering the study * Participants may not h