Alisertib and Fulvestrant in Treating Patients With Hormone Receptor Positive Breast Cancer That is Metastatic or Locally Advanced and Cannot Be Removed by Surgery

Inclusion Criteria: * Histologic proof of metastatic or locally advanced, unresectable breast cancer which is estrogen receptor positive and/or progesterone positive per institutional standards * Non-measurable or measurable disease * Post-menopausal women, as verified by: * Post bilateral surgical oophorectomy, or * No spontaneous menses \>= 1 year, or * No menses for \< 1 year with follicle-stimulating hormone (FSH) and estradiol levels in postmenopausal range, according to institutional standards * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet (PLT) \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 upper limit of normal (ULN) * Alanine transaminase (ALT) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement) * Creatinine =\< 1.5 x ULN * Hemoglobin \>= 9.0 gm/dL * Calculated creatinine clearance must be \>= 45 ml/min using the Cockcroft-Gault formula * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Ability to provide informed written consent * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Life expectancy \>= 4 months * Willing to provide tissue samples for research purposes * Prior therapies: * All women: at least one prior line of hormonal therapy for de novo disease (stage IV metastatic at diagnosis, no prior adjuvant therapy) or relapse \> 1 year after completion of adjuvant therapy; relapse on adjuvant hormonal therapy will count as the one prior line of therapy * All women: at least 1 prior line of chemotherapy in the adjuvant and/or metastatic setting, but not more than 2 regimens in the metastatic setting * Capable of swallowing tablets Exclusion Criteria: * Known standard therapy for the patient's disease that is potentially curative or definitely capable of extending life expectancy * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Any of the following prior therapies: * Chemotherapy =\< 21 days prior to registration * Mitomycin C/nitrosoureas =\< 42 days prior to registration * Immunotherapy =\< 28 days prior to registration * Biologic therapy =\< 28 days prior to registration * Radiation therapy =\< 21 days prior to registration * Radiation to \> 25% of bone marrow prior to registration * Hormonal therapy =\< 14 days prior to registration * Failure to recover to grade =\< 1 from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * Uncontrolled central nervous system (CNS) metastases * NOTE: metastases have been treated by surgery and/or radiotherapy and patients have been neurologically stable and off of steroids \> 12 weeks are eligible * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation) * 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 * Immunocompromised patients and patients known to be human immunodeficiency virus (HIV) positive and currently receiving antiretroviral therapy; NOTE: patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Other active malignancy =\< 5 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: patients must not be receiving other active treatment for another cancer * History of myocardial infarction =\< 6 months prior to registration, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * \> 2 prior chemotherapy regimens * Any prior treatment with an aurora kinase inhibitor (either an aurora A kinase or pan-aurora kinase inhibitor) * Plans to begin bisphosphonates or denosumab after registration or began therapy regiment =\< 30 days from registration * NOTE: patients on a stable dose of bisphosphonates or denosumab \> 30 days prior to registration are acceptable * Prior allogeneic bone marrow or organ transplantation * 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 * Known 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 * Requirement for constant administration of proton pump inhibitor, histamine-2 (H2) antagonist, or pancreatic enzymes; histamine-2 (H2) receptor antagonists are not permitted from the day prior (day -1) through to the end of alisertib dosing (e.g., day 7), except as required for premedication for a protocol-specific agent (e.g., taxane); neutralizing antacids and calcium-containing supplements cannot be taken from 2 hours prior to alisertib dosing until up to 2 hours after dosing * Systemic infection requiring intravenous (IV) antibiotic therapy within 14 days preceding the first dose of study drug, or other severe infection * Myocardial infarction within 6 months prior to enrollment or has 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; prior to study entry, any electrocardiogram (ECG) abnormality at screening has to be documented by the investigator as not medically relevant * 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 within 14 days prior to the first dose of alisertib and during the study * Known history of human immunodeficiency virus (HIV) infection, hepatitis B, or hepatitis C; testing is not required in the absence of clinical findings or suspicion * Receipt of corticosteroids within 7 days prior to the first dose of study treatment, unless patient has been taking a continuous dose of no more than 15 mg/day of prednisone for at least 1 month prior to first dose of study treatment; low dose steroid use for the control of nausea and vomiting will be allowed; topical steroid use is permitted; inhaled steroids are permitted * Inability to swallow oral medication or inability or unwillingness to comply with the administration requirements related to alisertib * Administration of myeloid growth factors or platelet transfusion within 14 days prior to the first dose of study treatment * Other severe acute or chronic medical or psychiatric condition, including uncontrolled diabetes, malabsorption, resection of the pancreas or upper small bowel, requirement for pancreatic enzymes, any condition that would modify small bowel absorption of oral medications, or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this study