Alisertib in Treating Patients With Recurrent or Persistent Leiomyosarcoma of the Uterus

Inclusion Criteria: * Patients must have incurable recurrent or persistent uterine leiomyosarcoma; histologic confirmation of the original primary tumor is required * Patients must have measurable disease; measurable disease is defined by Response Evaluation Criteria in Solid Tumors (RECIST) (version 1.1); measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI), or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Patients must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST version 1.1; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Patients must not be eligible for a higher priority Gynecologic Oncology Group (GOG) protocol, if one exists; in general, this would refer to any active GOG phase III protocol for the same patient population (12/10/2012) * Patients who have received one prior regimen must have a GOG performance status of 0, 1, or 2; patients who have received two prior regimens must have a GOG performance status of 0 or 1 * Patients should be free of active infection requiring antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]) * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration * Any other prior therapy directed at the malignant tumor, including chemotherapy and immunologic agents, must be discontinued at least three weeks prior to registration (12/10/2012) * Any prior radiation therapy must be discontinued at least four weeks prior to registration (12/10/2012) * Patients must have had at least one prior chemotherapeutic regimen for management of leiomyosarcoma * Patients are allowed to receive, but are not required to receive, one additional cytotoxic regimen for management of recurrent or persistent disease (12/10/2012) * Patients must NOT have received any prior therapy directed at Aurora kinase for management of recurrent or persistent disease; patients who were treated on GOG-0250 (gemcitabine + docetaxel plus bevacizumab vs placebo) are eligible; treatment on GOG-0250 would count as ONE prior regimen * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Serum creatinine =\< institutional upper limit of normal (ULN) OR creatinine clearance \>= 60 mL/min/1.73m\^2 (calculated or measured) * Bilirubin =\< ULN * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x ULN * Alkaline phosphatase =\< 2.5 x ULN * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients of childbearing potential must have a negative serum pregnancy test prior to the study entry and be practicing an effective form of contraception; pregnant women are excluded from this study * Patients must be able to take oral medication and to maintain a fast for 2 hours before and 1 hour after MLN8237 administration * Patient must not have taken agents that effect gastric pH within 4 days (any proton pump inhibitor), or 1 day (any histamine-2 antagonist) of the planned start of therapy; patients must be able to avoid all other types of antacids for 2 hours before and 2 hours after each dose of MLN8237 Exclusion Criteria: * Patients who have had prior therapy with MLN8237 or taken part in a study of an investigational compound or device within 4 weeks of entering this study * Patients who have had surgery (excluding biopsy), radiotherapy, or chemotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to the planned start of protocol treatment or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier; patients who have had hormonal agents within 1 week of the planned start of protocol treatment * Patients with other invasive malignancies, with the exception of non-melanoma skin cancer, carcinoma in situ of the cervix, or ductal carcinoma in situ of the breast, are excluded if there is any evidence of other malignancy being present within the last three years * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of uterine leiomyosarcoma within the last three years are excluded; thus, patients with a history of prior pelvic radiation for uterine leiomyosarcoma are eligible; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients who have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of uterine leiomyosarcoma within the last three years are excluded; patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and that the patient remains free of recurrent or metastatic disease * Patients who are nursing because there is an unknown but potential risk for adverse events in nursing infants from MLN8237 * Patients with a history of central nervous system metastases and/or carcinomatous meningitis * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to MLN8237, including but not limited to established allergic reaction to benzodiazepines * Patients who are known to be human immunodeficiency virus (HIV) positive * Patients who have had prior allogeneic bone marrow or organ transplantation * Patients with a 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; or any conditions that could result in excessive toxicity associated with the benzodiazepine-like effects of MLN8237 * Patients who require constant administration of proton pump inhibitor, H2 antagonist, or pancreatic enzymes; intermittent uses of antacids or H2 antagonists are allowed * Patients who are unable to swallow oral medication or to maintain a fast as required for 2 hours before and 1 hour after MLN8237 administration or any condition that would modify small bowel absorption of oral medications, including malabsorption, or resection of pancreas or upper bowel * Patients who have had treatment with clinically significant enzyme inducers, such as the enzyme-inducing antiepileptic drugs phenytoin, carbamazepine, oxcarbazepine, primidone or phenobarbital, or rifampin, rifabutin, rifapentine, or St. John's wort within 14 days prior to the first dose of MLN8237 and during the study * Patients who have had a myocardial infarction within 6 months prior to enrollment or have New York Heart Association (NYHA) class III (marked limitation of physical activity, comfortable at rest, but less than ordinary activity causes fatigue, palpitation, or dyspnea) or IV (unable to carry out any physical activity without discomfort, symptoms of cardiac insufficiency at rest, if any physical activity is undertaken, discomfort is increased) 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 * Patients must limit alcohol consumption to no more than 1 standard unit of alcohol (12 oz beer \[350 mL\], 1.5 oz \[45 mL\] of 80-proof alcohol, or one 6-oz \[175 mL\] glass of wine) per day during the study and for 30 days from the last dose of MLN8237; patients who are unable to comply with these restrictions are not eligible