Abemaciclib for Bone and Soft Tissue Sarcoma With Cyclin-Dependent Kinase (CDK) Pathway Alteration

Inclusion Criteria: 1. Diagnosis of soft tissue sarcoma or conventional chondrosarcoma, dedifferentiated chondrosarcoma, chordoma, or osteosarcoma (see exclusion criteria below) 2. Metastatic or locally advanced disease that is unresectable 3. There is no limit to the number of prior therapies a subject may have had, but the following requirements must be met: 1. Conventional chondrosarcoma low-grade osteosarcoma, and chordoma: No requirements regarding prior therapy 2. Osteosarcoma (high-grade), Dedifferentiated chondrosarcoma: at least 1 prior anthracycline chemotherapy, alone or in combination, required either as adjuvant, neoadjuvant or in the metastatic setting. If anthracycline chemotherapy is contraindicated, alternative prior first line chemotherapy is acceptable. 3. Soft tissue sarcoma: at least 1 line of systemic therapy, unless the sarcoma subtype is one that is generally considered unresponsive to standard chemotherapy. 4. Age ≥ 18 years. 5. Provide study specific (step 1) informed consent prior to study entry 6. Documented CDK pathway abnormality on a commercially available mutation profiling test (Foundation, Tempus xT, etc), if performed previously as part of routine/standard care on tumor (metastatic or primary), having at least one of the following (a and/or b) 1. Cyclin D1 (CCND1), cyclin D2 (CCND2), cyclin D3 (CCND3), cyclin dependent kinase 4 (CDK4), and/or cyclin dependent kinase 6 (CDK6) amplification/copy number gain 2. Cyclin Dependent Kinase Inhibitor 2A (CDKN2A) or CDKN2B copy number loss 7. Provide study-specific (step 2) informed consent 8. Rb positive confirmed by immunohistochemistry testing of archived tumor tissue specimen (metastatic or primary site) performed centrally at Medical College of Wisconsin Precision Medicine Laboratory. 9. All subjects must have measurable disease as defined by RECIST 1.1. (See RECIST 1.1 criteria in Appendix 10. 10. Subjects must also have had evidence of disease progression by RECIST 1.1 within 6 months of enrollment, or newly diagnosed within the last 6 months (refer to step 1 criteria regarding previous lines of therapy). 11. A washout period of at least 21 days is required between last chemotherapy dose and enrollment. 12. A washout period of at least 14 days is required between end of radiotherapy and enrollment. 13. At least 14 days after surgery, and absence of significant wound healing issues that would pose infection risk. 14. Subjects with brain metastasis that have been treated with definitive surgery or radiation and have been clinically stable for 3 months are eligible. 15. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 16. Adequate organ and marrow function as defined below (ULN indicates institutional upper limit of normal): * Hemoglobin ≥ 8.0 g/dL a. 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. * Platelets ≥ 100 x 10\^9/L * Total bilirubin ≤ 1.5 x ULN a. Patients with Gilbert's syndrome with a total bilirubin ≤2.0 times ULN and direct bilirubin within normal limits are permitted. * Aspartate aminotransferase (AST)(SGOT)/alanine aminotransferase (ALT)(SGPT) ≤ 3 x institutional ULN * Renal function (at least one of the following): Estimated Creatinine Clearance (CrCl) ≥ 30 mL/min (Cockcroft-Gault), estimated glomerular filtration rate (eGFR) ≥ 30 mL/min/1.73 m\^2 (MDRD or Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula), or actual CrCl as determined by 24-hour urine collection 17. Female subjects must meet one of the following: * Postmenopausal for at least one year before enrollment, OR * Surgically sterile (i.e. undergone a hysterectomy or bilateral oophorectomy), OR * If subject is of childbearing potential (defined as not satisfying either of the above two criteria), must have a negative serum pregnancy test within 21 days of step 2 enrollment AND * Agree to practice two acceptable methods of contraception (combination methods requires use of two of the following: diaphragm with spermicide, cervical cap with spermicide, contraceptive sponge, male or female condom with spermicidal agent added, hormonal contraceptive) from the time of signing of the informed consent form through 90 days after the last dose of study agent, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] and withdrawal are not acceptable contraception methods.) 18. Male subjects, even if surgically sterilized (i.e., status post vasectomy), must agree to one of the following: * Practice effective barrier contraception during the entire study period and through 60 calendar days after the last dose of study agent, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post ovulation methods\] and withdrawal are not acceptable methods of contraception.) 19. Subjects must be deemed able to comply with the study plan by the local PI. 20. Ability to swallow oral medications Exclusion Criteria: 1. Diagnosis of well differentiated (WD) or dedifferentiated (DD) liposarcoma 2. Prior treatment with a specific CDK 4 or CDK 6 inhibitor - (such as palbociclib, abemaciclib, or ribociclib). 3. Subjects who have not recovered (Common Terminology Criteria for Adverse Events \[CTCAE v5.0\] Grade ≤1) from the acute effects of chemotherapy (except for residual alopecia or Grade 2 peripheral neuropathy) prior to enrollment, or other toxicity or serious preexisting medical condition(s) (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, history of major surgical res