Alisertib With or Without Fulvestrant in Treating Patients With Locally Advanced or Metastatic, Endocrine-Resistant Breast Cancer

Inclusion Criteria: * PRE-REGISTRATION ELIGIBILITY * Post-menopausal defined as * Age \>= 60 and amenorrhea \> 12 consecutive months, OR * Age \< 60 and amenorrhea \> 12 consecutive months without another cause and documented follicle stimulating hormone (FSH) level of \> 35 mIU/mL, OR * Previous bilateral oophorectomy * Histologic proof of metastatic or locally advanced, unresectable breast cancer * History of ER positive (+) (\>= 10% of cells positive on hematoxylin and eosin stain \[H\&E\]), HER2 negative (-) breast cancer disease, either as a * History of primary, operable ER+/HER2- invasive breast cancer OR * History of de novo metastatic breast cancer that is ER+/HER2- * Note: HER2- (negative) disease defined as one of the following: * HER2 immunohistochemistry (IHC) expression of 0, 1+ and in-situ hybridization (ISH) non-amplified * HER2 IHC expression of 0, 1+ and ISH not done * HER2 IHC expression of 2+ and ISH non-amplified * IHC not done and ISH non-amplified * Prior treatment * No more than two prior chemotherapy regimens in the metastatic setting * Prior treatment with fulvestrant in the metastatic setting is required, except for patients with a history of ER-negative metastatic breast cancer * Unlimited prior endocrine therapy regimens in the metastatic setting are allowed * No prior treatment with an aurora Kinase inhibitor (either an aurora A or pan-aurora kinase inhibitor) * Disease that is measurable where: * A non-nodal lesion is considered measurable if its longest diameter can be accurately measured as \>= 2.0 cm with chest x-ray, or as \>= 1.0 cm with computed tomography (CT) scan, CT component of a positron emission tomography (PET)/CT, or magnetic resonance imaging (MRI) * A malignant lymph node is considered measurable if its short axis is \>= 1.5 cm when assessed by CT scan (CT scan slice thickness recommended to be no greater than 5 mm); Note: tumor lesions in a previously irradiated area are not considered measurable disease; Note: disease that is measurable by physical examination only is not eligible * No history of tumors involving spinal cord or heart * History of brain metastases as per the following criteria: * Patients with a history of resected brain metastases are eligible only if they are asymptomatic and have stable MRI scans for 3 consecutive months, including \< 28 days prior to pre-registration * Patients who receive stereotactic radiosurgery or whole brain radiation for brain metastases are eligible only if they are asymptomatic and have stable MRI scans for 3 consecutive months, including \< 28 days prior to pre-registration * Fully recovered from acute, reversible effects of prior therapy regardless of interval since last treatment; * EXCEPTION: neuropathies - if grade 2 neuropathies have been stable for at least 3 months since completion of prior treatment patient is eligible * Eastern Cooperative Oncology Group (ECOG) performance status: 0, 1, 2 * Not receiving administration of proton pump inhibitor, H2 antagonist, or pancreatic enzymes * Willing to limit daily alcohol intake to the following: one 12-oz glass of beer, one 6-oz glass of wine, or one 1.5-oz portion of 80-proof alcohol * No uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Uncontrolled symptomatic cardiac arrhythmia * Uncontrolled hypertension (defined as blood pressure \> 160/90) * No history of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease; requirement for supplemental oxygen * No other active second malignancy other than non-melanoma skin cancers and in situ cervical cancers within 5 years of registration * NOTE: A second malignancy is not considered active if all treatment for that malignancy is completed and the patient has been disease-free for at least 5 years prior to registration * Ability to provide written informed consent * Willing to return to enrolling institution for follow-up during the active treatment; event monitoring following completion of therapy may occur outside the enrolling institution * No history of myocardial infarction =\< 6 months prior to pre-registration or New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities * No prior allogeneic bone marrow or organ transplantation * No known clinical finding or suspicion of human immunodeficiency virus (HIV) infection, hepatitis B, or hepatitis C * No co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Able to swallow oral medication * No known gastrointestinal (GI) disease or GI procedures that could interfere with the oral absorption or tolerance of alisertib; examples include, but are not limited to partial gastrectomy, history of small intestine surgery, and celiac disease * No visceral crisis: Visceral crisis is not the mere presence of visceral metastases, but implies severe organ dysfunction as assessed by symptoms and signs, laboratory studies, and rapid progression of disease * No requirement for constant administration of proton pump inhibitor, H2 antagonist, or pancreatic enzymes * Willing to undergo a biopsy of a metastatic site of breast disease for central laboratory determination of ER and correlative research purposes * REGISTRATION ELIGIBILITY CRITERIA * =\< 28 days post pre-registration * Central ER determination on pre-registration biopsy completed * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 9.0 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine transaminase (ALT) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement) * Calculated creatinine clearance must be \>= 45 ml/min using the Cockcroft-Gault formula * Willing to provide blood and tissue for correlative research purposes Exclusion Criteria: * REGISTRATION EXCLUSION CRITERIA * Any of the following therapies prior to registration: * Chemotherapy =\< 21 days * Immunotherapy =\< 21 days * Biologic therapy =\< 21 days * Hormonal therapy =\< 14 days * Monoclonal antibodies =\< 14 days * Radiation therapy =\< 14 days * Administration of myeloid growth factors or platelet transfusion =\< 14 days prior to registration * Systemic infection requiring intravenous (IV) antibiotic therapy =\< 14 days prior to registration * Treatment with clinically significant enzyme inducers, such as the enzyme-inducing antiepileptic drugs phenytoin, carbamazepine or phenobarbital, or rifampin, rifabutin, rifapentine or St. John's wort =\< 14 days prior to registration * Receipt of corticosteroids =\< 7 days prior to registration, unless patient has been taking a continuous dose of no more than 15 mg/day of prednisone for at least 30 days prior to registration