Pembrolizumab and Binimetinib in Treating Patients With Locally Advanced or Metastatic Triple Negative Breast Cancer

Inclusion Criteria: * Age \>= 18 years * Histological confirmation of adenocarcinoma of the breast * Estrogen receptor (ER) and progesterone receptor (PR) negative; defined as ER =\< 10% and PR =\< 10% staining by immunohistochemistry (IHC) * HER2 negative in the primary or metastatic tumor tissue defined as: * Immunohistochemistry (IHC) grade 0 as defined by no staining observed or membrane staining that is incomplete and is faint/barely perceptible and within =\< 10% of the invasive tumor cell; OR * IHC 1+ as defined by incomplete membrane staining that is faint/barely perceptible and within \> 10% of the invasive tumor cell; OR * IHC grade 2+ staining intensity by means of IHC analysis with no gene amplification below; OR * No gene amplification on in situ hybridization (ISH) based on: * Single-probe average HER2 copy number \< 4.0 signals/cell OR * Dual-probe HER2/CEP17 ratio \< 2.0 with an average HER2 copy number \< 4.0 signals/cell * For phase II part of the trial: =\< 3 prior lines of treatment in the metastatic setting for the current breast cancer; however, there is no limit on number of prior line of therapy in phase I part of the trial * Measurable disease * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Hemoglobin \>= 9.0 g/dL (must be \>= 7 days after most recent transfusion) (obtained =\< 14 days prior to registration) * Absolute neutrophil count (ANC) \>= 1500/mm\^3 or \>= 1.5 x 10\^9/L (obtained =\< 14 days prior to registration) * Platelet count \>= 100,000/mm\^3 or \>= 100 x 10\^9/L (must be \>= 7 days after most recent transfusion) (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to registration) * Aspartate transaminase (AST) and/or alanine transaminase (ALT) =\< 2.5 x ULN or =\< 5 x ULN for patients with liver metastases (obtained =\< 14 days prior to registration) * Creatinine =\< 1.5 x ULN OR calculated creatinine clearance must be \>= 50 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to registration) * International normalized ratio (INR) or prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (obtained =\< 14 days prior to registration) * Adequate cardiac function: * Left ventricular ejection fraction (LVEF) \>= 50% as determined by multigated acquisition (MUGA) scan or echocardiogram (echo) * Corrected QT (QTc) interval =\< 480 ms * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Able to swallow oral medication * Both female and male patients of reproductive potential must agree to avoid pregnancy or impregnating a partner (respectively) while receiving drug and for 120 days after last dose of study drug * Provide written informed consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willing to provide mandatory tissue and blood for correlative research purposes * RETREATMENT REGISTRATION: Treatment cannot begin prior to registering to the retreatment phase and will ideally begin =\< 7 days after registration for the retreatment phase * RETREATMENT REGISTRATION: Stopped initial treatment with pembrolizumab and binimetinib after attaining an investigator-determined confirmed complete response (CR) according to RECIST 1.1, and: * Was treated for at least 24 weeks with pembrolizumab and binimetinib before discontinuing therapy * Received at least 2 cycles with pembrolizumab and binimetinib beyond the date when the initial CR was declared OR * Had stable disease (SD), partial response (PR), or CR and stopped pembrolizumab and binimetinib treatment after 24 months of study therapy for reasons other than disease progression or intolerability * RETREATMENT REGISTRATION: ECOG performance status (PS) 0 or 1 * RETREATMENT REGISTRATION: Hemoglobin \>= 9.0 g/dL (must be \>= 7 days after most recent transfusion) (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Absolute neutrophil count (ANC) \>= 1500/mm\^3 or \>= 1.5 X 10\^9/L (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Platelet count \>= 100,000/mm\^3 or \>= 100 X 10\^9/L (must be \>= 7 days after most recent transfusion) (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Total bilirubin =\< 1.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Aspartate transaminase (AST) and alanine transaminase (ALT) =\< 2.5 x ULN or =\< 5 x ULN for patients with liver metastases (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Creatinine =\< 1.5 x ULN OR calculated creatinine clearance must be \>= 50 ml/min using the Cockcroft-Gault formula (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: International normalized ratio (INR) or prothrombin time (PT) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless patient is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (obtained =\< 14 days prior to re-registration) * RETREATMENT REGISTRATION: Females of childbearing potential should have a negative serum or urine pregnancy test =\< 72 hours prior to re-registration * RETREATMENT REGISTRATION: Females or males of childbearing potential must be willing to use adequate methods of contraception or abstain from heterosexual activity for the course of the study through 120 days after last dose of study medication * RETREATMENT REGISTRATION: Experienced an investigator-determined confirmed radiographic disease progression after stopping their initial treatment with pembrolizumab and binimetinib Exclusion Criteria: * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm OR participated in a study of an investigational agent, received study therapy or used an investigational device =\< 4 weeks prior to registration * Immunocompromised patients and patients with known immunodeficiency; or receiving systemic steroid therapy or any other immunosuppressive therapy =\< 7 days prior to registration; NOTE: inhaled steroids and low-dose corticosteroids are allowed * History of active tuberculosis (TB), human immunodeficiency virus (HIV), active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) and/or active hepatitis C infection (e.g. hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] qualitative is detected) * Received a live vaccine =\< 30 days prior to registration; NOTE: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines, and are not allowed * Hypersensitivity to pembrolizumab, binimetinib, or any excipients of either drug * Prior anti-cancer therapy with a monoclonal antibody (mAb) =\< 4 weeks prior to registration OR failure to recover (to =\< grade 1) from adverse events (AE) attributable to agents received \> 4 weeks prior to registration * Prior therapy including chemotherapy, targeted small molecule therapy or radiation therapy =\< 2 weeks prior to registration OR failure to recover (to =\< grade 1 or to baseline) from adverse events (AE) attributable to agents received \> 4 weeks prior to registration; NOTE: exception for neuropathy =\< grade 2, which is allowed * Any active central nervous system (CNS) lesion (i.e., those with radiographically unstable, symptomatic lesions) and/or leptomeningeal metastases; NOTE: patients treated with stereotactic radiotherapy or surgery are eligible if no evidence of CNS disease progression \>= 4 weeks and patients must be off corticosteroid therapy for \>= 3 weeks; NOTE: carcinomatous meningitis is excluded regardless of clinical stability * Active autoimmune disease requiring systemic treatment in the past 2 years (i.e. use of disease modifying agents, corticosteroids or immunosuppressive drugs); NOTE: 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 * Known history of, or any evidence of active, non-infectious pneumonitis * Active infection requiring systemic therapy * Known history of acute or chronic pancreatitis * History of or current evidence of retinal vein occlusion (RVO) or predisposing factors to RVO (e.g. uncontrolled glaucoma or ocular hypertension, history of hyperviscosity or hypercoagulability syndromes) * History of retinal degenerative disease * History of Gilbert's syndrome * Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: adequately treated non-melanotic skin cancer (adequate wound healing is required prior to study entry) or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior solid tumor malignancy, it must have been treated curatively with no evidence of recurrence =\< 3 years prior to registration * Impaired cardiovascular function or clinically specific cardiovascular disease including any of the following: * History of acute coronary syndromes (including myocardial infarction unstable angina, coronary artery bypass grafting, coronary angioplasty, or stenting) =\< 6 months; OR * Symptomatic chronic heart failure history or current evidence of clinically significant cardiac arrhythmia and/or conduction abnormality \< 6 months prior to screening; except atrial fibrillation and paroxysmal supraventricular tachycardia * Uncontrolled arterial hypertension defined as persistent elevation of systolic blood pressure \>= 150 mmHg or diastolic blood pressure \>= 100 mmHg despite medical treatment * History of neuromuscular disorders that are associated with elevated creatine kinase (CK) (e.g., inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy) * Planning to embark on a new strenuous exercise regimen after first dose of study treatment; NOTE: muscular activities, such as strenuous exercise, that can result in significant increases in plasma CK levels should be avoided while on binimetinib treatment * Impairment of gastrointestinal function or gastrointestinal disease (e.g., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small bowel resection); NOTE: gastric bypass is allowed * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/psychological issues, etc. * Major surgery =\< 3 weeks prior to registration or failure to adequately recover from surgery * Medical, psychiatric, cognitive or other conditions that may compromise the patient's ability to understand the patient information, give informed consent, comply with the study protocol or complete the study * RETREATMENT REGISTRATION: Received any type anti-cancer treatment since the last dose of pembrolizumab * RETREATMENT REGISTRATION: History or current evidence of any condition, therapy, or laboratory abnormality that might interfere with subject's participation for the full duration of the trial or is not in the best interest of the subject to participate, in the opinion of the treating investigator