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 have had radiotherapy within 1 week prior to entering the study. Patients may not have had \> 25% of their bone marrow radiated. Stereotactic radiosurgery (SRS) within 1 week prior to entering the study will be allowed * Participants may not have received tyrosine kinase inhibitors (TKIs) or small molecules within 5 half-lives or 2 weeks (whichever is shorter) of study entry * Patients who have experienced adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) must have recovered, with the exception of alopecia or as otherwise specified in the eligibility criteria * The effects of the combination of ZEN003694 (ZEN-3694) and MK-3475 on the developing human fetus are unknown. For this reason and because BETi and PD-1 blocking agents as well as 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, for the duration of study participation, and for 6 months after study completion. 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 6 months after completion of ZEN003694 (ZEN-3694), MK-3475 and nab-Paclitaxel administration. Female subjects of childbearing potential must have a negative serum or urine pregnancy test within 2 weeks prior to registration. Childbearing potential is defined as: participants who have not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause) and have not undergone surgical sterilization (removal of ovaries and/or uterus) * 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 Exclusion Criteria: * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ZEN003694 (ZEN-3694), nab-paclitaxel, or pembrolizumab * Patients with uncontrolled intercurrent illness * Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Any gastrointestinal (GI) disorder that may affect absorption of oral medications in the opinion of the treating investigator, such as malabsorption syndrome or major bowel or stomach resection * Pregnant women are excluded from this study because ZEN003694 (a BETi agent) and MK-3475 have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ZEN003694 (ZEN-3694), breastfeeding should be discontinued if the mother is treated with ZEN003694 (ZEN-3694). These potential risks may also apply to MK-3475 and nab-paclitaxel * Patients who have previously received ZEN003694 (ZEN-3694) or who have been treated with an investigational BET inhibitor * DOSE EXPANSION COHORT: Prior exposure to immune checkpoint inhibitors in the metastatic setting. PD-1 or PD-L1 inhibitors in the neo-/adjuvant setting are allowed if at least 12 months have elapsed since the end of adjuvant systemic treatment to development of metastatic disease * DOSE EXPANSION COHORT: Prior exposure to taxane-based therapy in the metastatic setting. Taxane in the neo-/adjuvant setting is allowed if at least 12 months have elapsed since the end of adjuvant systemic treatment to development of metastatic disease * Patients receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 are ineligible. Strong inhibitors or inducers of CYP3A4 must be discontinued at least 7 days prior to the first dose of ZEN003694 (ZEN-3694). Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Patients receiving any medications or substances that are Factor Xa inhibitors (i.e., rivaroxaban, apixaban, betrixaban, edoxaban otamixaban, letaxaban, eribaxaban) and Factor IIa inhibitors (i.e., dabigatran). Low molecular weight heparin is allowed * Patients who have had a bone-targeted radionuclide within 6 weeks of the first dose of ZEN003694 (ZEN-3694) * Myocardial infarction or unstable angina within 6 months prior to the first dose of ZEN003694 (ZEN-3694) * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. The use of physiologic doses of corticosteroids may be approved after consultation with the study principal investigator (PI) * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis * Has a known history of active tuberculosis (TB) * Has received a live vaccine within 30 days of planned treatment start. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster, yellow fever, rabies, Bacille Calmette-Guerin (BCG), and typhoid vaccine. Seasonal flu vaccines that do not contain live virus are permitted. Coronavirus disease-2019 (COVID-19) vaccines received within the last 30 days are also permitted * Participants with known or suspected extensive bone marrow infiltration per radiographic assessment, laboratory assessment, or bone marrow sampling (e.g., aspiration or biopsy), determined to be clinically significant by the treating investigator