Testing the Use of Fulvestrant and Binimetinib Targeted Treatment for NF1 Mutation in Hormone Receptor-Positive Metastatic Breast Cancer (A ComboMATCH Treatment Trial)

Inclusion Criteria: * Patient must have enrolled onto EAY191 and must have been given a treatment assignment to ComboMATCH to EAY191-N2 based on the presence of an actionable mutation as defined in EAY191 * The patient must be enrolled on the ComboMATCH Master Registration Trial EAY191 * Note: Patients must fulfill all eligibility criteria outlined in the ComboMATCH Registration Trial EAY191 at the time of registration to EAY191-N2. This includes submission of next-generation sequencing (NGS) data from one of the National Cancer Institute (NCI) credentialed designated laboratories for all potential patients prior to treatment trial assignment. Copy number and allele frequency cutoff as per the Registration protocol * Patients must have disease that can be safely biopsied and agree to a pre-treatment biopsy or, if disease cannot be safely biopsied, have archival tissue available from within 12 months prior to the date of registration on the ComboMATCH registration trial (EAY191) * Please note the current actionable marker of interest (aMOI)/actionable alteration list for this treatment trial can be found on the Cancer Trial Support Unit (CTSU) ComboMATCH Registration protocol page * Please note novel/Dynamic aMOI can be submitted for review per the process described in the ComboMATCH Registration protocol * A COMBOMATCH TREATMENT TRIAL EAY191-N2 ELIGIBILITY CRITERIA: * The patient or a legally authorized representative must provide study-specific informed consent prior to study entry and, for patients treated in the United States (U.S.), authorization permitting release of personal health information * Age \>= 18 * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Histologically or cytologically confirmed invasive breast carcinoma * Confirmed metastatic disease by either imaging or tissue diagnosis * Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 and one additional lesion that can be biopsied (primary, metastatic both allowed) * Patients must have inactivating or inferred inactivating NF1 alterations detected in tumor as determined by the ComboMATCH screening assessment * The tumor must have been determined to be estrogen receptor (ER) and/or progesterone receptor (PgR) positive assessed by current American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guideline recommendations for hormone receptor testing. Patients with \>= 1% ER or PgR staining by immunohistochemistry (IHC) are considered positive * The tumor must have been determined to be HER2-negative by current ASCO/CAP guidelines * Prior use of CDK4/6 inhibitor(i) is required * Prior use of fulvestrant regardless of duration is allowed and will determine treatment assignment * Up to one line of chemotherapy in metastatic setting is allowed * Absolute neutrophil count \>= 1,500/mm\^3 * Platelet count \>= 100,000/ mm\^3 * Hemoglobin level \>= 10 g/dL * Creatinine clearance (CrCL) of ≥ 30 mL/min by the Cockcroft-Gault formula * Total bilirubin level =\< institutional upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) must be =\< 5.0 x ULN * For patients who will be assigned to Cohort 2 (fulvestrant-resistant), a left ventricular ejection fraction (LVEF) assessment must be performed within 12 weeks prior to registration. The LVEF must be \>= 50% regardless of the cardiac imaging facility's lower limit of normal. (LVEF assessment performed by echocardiogram is preferred; however, MUGA scan may be substituted based on institutional/situational preferences) * 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 * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial * ELIGIBILITY CRITERIA FOR COHORT 1, TREATMENT REGIMEN 2 PATIENTS WHO MIGRATE TO COHORT 2: Cohort migration: Patients treated with control treatment fulvestrant who experience disease progression may be eligible to migrate to Cohort 2 and receive combination treatment with binimetinib and fulvestrant. Patients who choose to do so must meet laboratory values and performance status requirements below and should begin treatment within 28 days * PATIENTS WHO MIGRATE TO COHORT 2: Patient's willingness to migrate to Cohort 2 affirmed * PATIENTS WHO MIGRATE TO COHORT 2: The patient must have an ECOG performance status of 0-2 * PATIENTS WHO MIGRATE TO COHORT 2: Absolute neutrophil count \>= 1,500/mm\^3 * PATIENTS WHO MIGRATE TO COHORT 2: Platelet count \>= 100,000/ mm\^3 * PATIENTS WHO MIGRATE TO COHORT 2: Hemoglobin level \>= 10 g/dL * PATIENTS WHO MIGRATE TO COHORT 2: Total bilirubin level =\< institutional upper limit of normal (ULN) * PATIENTS WHO MIGRATE TO COHORT 2: AST and ALT must be =\< 5.0 x ULN * PATIENTS WHO MIGRATE TO COHORT 2: Creatinine clearance (CrCL) of ≥30 mL/min by the Cockcroft-Gault formula * PATIENTS WHO MIGRATE TO COHORT 2: A LVEF performed within the last 3 months must be \>= 50% regardless of the cardiac imaging facility's lower limit of normal (LVEF assessment performed by echocardiogram is preferred; however, MUGA scan may be substituted based on institutional/situational preferences) * PATIENTS WHO MIGRATE TO COHORT 2: Pregnancy test according to institutional standards must be negative (for patients of childbearing potential only) Exclusion Criteria: * Concurrent anticancer therapy * Active autoimmune disease requiring systemic treatment within the past 3 months, documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents * Active brain metastasis. Brain metastases that have been stable for at least 1 month after completion of treatment are not an exclusion criterion * History of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment/central serous, chorioretinopathy (CSCR), retinal vein occlusion (RVO), or neovascular macular degeneration * Patients will be excluded if they currently have the following risk factors for RVO that are documented prior to the enrollment: * Known uncontrolled glaucoma with intra-ocular pressures \>= 21 mmHg * Known serum cholesterol \>= grade 2. * Known hypertriglyceridemia \>= grade 2 * Known hyperglycemia (fasting) \>= grade 2 * Patients with baseline QT corrected for heart rate (QTc) \> 500 ms, either induced by medication or congenital long QT syndrome will be excluded due to known side effects of binimetinib * Nervous system disorder (paresthesia, peripheral motor neuropathy, or peripheral sensory neuropathy) \>= grade 2 * 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 2B or better * Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications * Other conditions that, in the opinion of the investigator, would preclude the patient from meeting the study requirements or interfere with interpretation of study results * Pregnancy or lactation at the time of registration or intention to become pregnant during the study (Note: Pregnancy testing according to institutional standards for patients of childbearing potential) * For binimetinib, highly effective contraception should be used for at least 30 days after the last dose, and patients should not breastfeed for 3 days after the last dose * For fulvestrant, highly effective contraception should be used for 1 year after the last dose, and patients should not breastfeed for 1 year after the last dose * Use of any investigational product within 30 days prior to study entry * INELIGIBILITY CRITERIA FOR COHORT 1, TREATMENT REGIMEN 2 PATIENTS WHO MIGRATE TO COHORT 2 * PATIENTS WHO MIGRATE TO COHORT 2: Not a candidate for binimetinib in the opinion of the treating investigator