Abemaciclib in Metastatic or Locally Advanced Anaplastic/Undifferentiated Thyroid Cancer

Inclusion Criteria: 1. Histologically or cytologically confirmed diagnosis of anaplastic thyroid cancer or undifferentiated thyroid cancer that does not have a known BRAF V600E positive on tissue/blood testing. BRAF V600E positive patients are eligible if they have previously received FDA approved therapy for this genetic abnormality and progressed or become intolerant. 2. Patients will be eligible if they meet either criteria: * Unresectable anaplastic thyroid cancer limited to the neck: Patients must have received radiation therapy or surgery to primary tumor and have subsequent evidence of anaplastic thyroid cancer (ATC). * Metastatic anaplastic thyroid cancer: either with entirely surgically removed cancer/metastatic only disease, or with disease in the neck not requiring radiation or surgery to the neck mass. 3. Patients with a bulky thyroid/neck mass and those in whom airway obstruction is suspected should undergo an evaluation via indirect or direct laryngoscopy to ensure patency of the trachea/airway prior to enrollment 4. Patients will not have any other curative therapeutic option, such as radiation or surgery. 5. Eastern Cooperative Oncology Group (ECOG) performance status 0-1. 6. Have measurable disease based on RECIST 1.1 7. Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion. Newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on Day 1. Subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived sample. 8. Be ≥ 18 years of age on day of signing informed consent. 9. Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade ≤1) from the acute effects of chemotherapy except for residual alopecia or Grade 2 peripheral neuropathy prior to study treatment start. A washout period of at least 21 days is required between last chemotherapy dose and study treatment start (provided the patient did not receive radiotherapy). 10. Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 14 days is required between end of radiotherapy and study treatment start. 11. The patient is able to swallow oral medications. 12. The patient has adequate organ function for all of the following criteria, Laboratory Value Guidance to Establish Adequate Organ Function System Laboratory Value Hematologic absolute neutrophil count (ANC)≥1.5 × 109/L Platelets≥100 × 109/L Hemoglobin≥8 g/dL Patients may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator. Initial treatment must not begin earlier than the day after the erythrocyte transfusion. Hepatic Total bilirubin ≤1.5 × upper limit of normal(ULN) Patients with Gilbert's syndrome with a total bilirubin ≤2.0 times ULN and direct bilirubin within normal limits are permitted. alanine aminotransferase (ALT) and aspartate aminotransferase (AST)≤3 × ULN 13. Women of childbearing potential and all men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) while taking drug and agree to continue for 3 months after the last dose of study treatment. Women of child bearing potential and male patients for 3 months should not mother or father a child in this period. A condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid. 14. Patient has the ability to understand and provide signed informed consent. 15. Willingness and ability to comply with scheduled visits, treatment plans, laboratory tests and other procedures. Exclusion Criteria: 1. Patients with known hypersensitivity to any of the excipients of abemaciclib 2. History of carcinomatous meningitis 3. Prior therapy with abemaciclib. 4. The patient has serious and/or uncontrolled preexisting medical condition(s) that, in the judgment of the investigator, would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, severe renal impairment \[e.g. estimated creatinine clearance \<30ml/min\], history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea). 5. Females who are pregnant or lactating. 6. The patient has active systemic bacterial infection (requiring intravenous \[IV\] antibiotics at time of initiating study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C \[for example, hepatitis B surface antigen positive\]. Screening is not required for enrollment. 7. The patient has a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest. 8. Presence or history of a malignant disease other than thyroid cancer that has been diagnosed and/or required therapy within the past year and is undergoing active anticancer treatment. Exceptions to this exclusion include the following: completely resected basal cell and squamous cell skin cancers, and completely resected carcinoma in situ of any type.