Testing the Addition of an Investigational Anti-Cancer Drug, ASTX660 (Tolinapant), to a Usual Chemotherapy Treatment (Eribulin) for Treatment of Advanced Triple Negative Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed invasive breast carcinoma. * We limit the molecular subtype to triple negative (TNBC) and hormone receptor-low and Her2 negative (hormone receptor \[HR\]-low/Her2\[-\]) breast cancer. TNBC is defined as: HER2 expression 0 or 1+ on immunohistochemistry (IHC) or non-amplified (defined as HER2/CEP17 ratio \< 2 or copy number \< 6) on fluorescence in situ hybridization (FISH). If HER2 expression is 2+ on IHC, negative HER2 expression must be confirmed by FISH. Pathologic diagnosis of TNBC (negative HER2 status by cytogenetics, \< 1% of cells stained positive for estrogen receptor \[ER\] by IHC, and \< 1% of cells stained positive for progesterone receptor \[PR\] by IHC) (Allison et al., 2020, Wolff et al., 2013). HR-low/Her2(-) is defined as: HER2 expression 0 or 1+ on IHC or non-amplified (defined as HER2/CEP17 ratio \< 2 or copy number \< 6) on fluorescence in situ hybridization (FISH). If HER2 expression is 2+ on IHC, negative HER2 expression must be confirmed by FISH. 1-10% of cells stained positive for ER by IHC, and/or 1-10% of cells stained positive for PR by IHC) (Allison et al., 2020, Wolff et al., 2013) * Patients must have confirmed locally advanced and unresectable or metastatic disease by either imaging or tissue diagnosis * Patients must have received at least 2 lines of systemic treatment for metastatic disease * Patients must have measurable disease according to the Response Evaluation Criteria in Solid Tumors (RECIST) guideline (version 1.1) criteria * Age ≥ 18 years. Because no dosing or adverse event data are currently available on the use of ASTX660 (tolinapant) in combination with eribulin mesylate in patients \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Leukocytes ≥ 3,000/mcL * Absolute neutrophil count ≥ 1,500/mcL * Platelets ≥ 100,000/mcL * Hemoglobin ≥ 9 g/dL * Total bilirubin ≤ 1.8 mg/dL * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional upper limit of normal (ULN) or ≤ 5 x institutional ULN if known liver metastases * Alkaline phosphatase ≤ 3 x institutional ULN or ≤ 5 x institutional ULN if known liver and/or skeletal metastases * Lipase ≤ 1.5 x ULN * Creatinine ≤ 1.5 x institutional ULN OR glomerular filtration rate (GFR) ≥ 60 mL/min/1.73 m\^2 * International normalized ratio (INR) ≤ 1.5 x ULN * Partial thromboplastin time (PTT) ≤ 1.5 x ULN * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial provided they are on a stable regimen of anti-retroviral therapy (ART) with no medications otherwise prohibited by this protocol (e.g., drug-drug interactions) * 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 there is no evidence of progression for at least 4 weeks after central nervous system (CNS)-directed treatment, as ascertained by clinical examination and brain imaging (MRI or CT) during the screening period * 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 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 II or better. Patients with history of known congestive heart failure (left ventricular ejection fraction \[LVEF\] \< 50%) must have documented LVEF ≥ 50% within 12 months of study enrollment * Patients with history of known type I or type II diabetes must have a fasting glucose level of \< 120 mg/dL on at least 2 separate occasions or glycosylated hemoglobin (HbA1c) \< 8.5% at screening within 14 days prior to registration * Patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to participate provided that their medication dose and INR/PTT is stable * Prophylactic antiemetics may be administered according to standard practice. The routine use of standard antiemetics, including 5-HT3 blockers, such as granisetron, ondansetron, or an equivalent agent, is allowed as needed, as long as corrected QT (QTc) interval on baseline electrocardiogram (ECG) \< 480 msec * Patients must be willing to have biopsies for this study in order to be enrolled in the dose expansion * The effects of ASTX660 (tolinapant) on the developing human fetus are unknown. For this reason and because dual IAP antagonist agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential must agree to practice 1 highly effective contraceptive measure of birth control (with a failure rate of \< 1% per year; preferably with low user dependency) during the study and for 6 months after the last dose of study treatment and must agree not to become pregnant for 6 months after completing treatment. Men with female partners of childbearing potential must agree to use a condom and advise their partners to practice 1 highly effective contraceptive measure of birth control (user dependent or with low user dependency) during the study and for at least 3 months after completing treatment, and must agree not to father a child while receiving study treatment and for at least 3 months after completing treatment * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants Exclusion Criteria: * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia * Patients who are receiving any other investigational agents or concurrent anticancer therapy * Patients who have had prior treatment with eribulin mesylate * Patients with pre-existing neuropathy of grade 2 or higher * Myeloid growth factors within 7 days prior to treatment start * Platelet transfusion within 7 days prior to treatment start * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ASTX660 (tolinapant) or other agents used in study * Immunosuppressive therapy is not allowed while on study * Systemic corticosteroid therapy at a daily dose higher than 15 mg prednisone or equivalent is not permitted while on study. Previous corticosteroid therapy must be stopped or reduced to the allowed dose at least 7 days prior to the CT/MRI screening. If a patient is on chronic corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed dose before the screening. Patients may be using topical or inhaled corticosteroids. Short-term (up to 7 days) systemic corticosteroids above 15 mg prednisolone or equivalent will be allowed for the management of acute conditions (e.g., treatment non-infectious pneumonitis) * Patients with non-healing wound, ulcer, or bone fracture. Patients with compression or pathologic fractures that are stable in the opinion of the investigator may be enrolled, as long as the bone fracture is not felt to pose a high likelihood of treatment delay or difficulties in treatment adherence as per the judgement of the investigator * Patients with active, clinically serious infections \> grade 2 (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\]5.0) (viral, bacterial or fungal infection) * History of known pneumocystis jiroveci pneumonia (PJP) infection or documented non-infectious pneumonitis/interstitial lung disease (ILD) * Patients with arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study medication * Uncontrolled hypertension (defined as blood pressure ≥ 150/90 mm/Hg) despite optimal medical management (per investigator's opinion) * Proteinuria as estimated by urine protein/creatinine ratio \> 3.5 g/g on random urine sample or grade ≥ 3 as assessed by 24-hour urine protein collection * Patients with history of, or current uncontrolled autoimmune disease. Patients who have adrenal or pituitary insufficiency who are stable on replacement therapy (i.e., thyroxine or physiologic corticosteroid replacement therapy that meets concomitant medication restrictions) are allowed * Patients with uncontrolled intercurrent illness or any other significant condition(s) that would make participation in this protocol unreasonably hazardous * Pregnant women are excluded from this study because ASTX660 (tolinapant) and eribulin mesylate are anti-cancer agents with 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 ASTX660 (tolinapant) and eribulin mesylate, breastfeeding should be discontinued until 2 weeks after the mother's last dose of study drugs * The patient has a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest * Patients with congenital long QT syndrome, bradyarrhythmias, or taking drugs known to prolong the QT interval * Patients unable to stop using any medication which is a moderate or strong CYP3A4 inhibitor or inducer within 2 weeks of the start of the study