Experimental drug plus radiation shows promise for rare sarcoma

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Subjects, \>= 18 years old, must have newly diagnosed or locally recurrent MDM2 or CDK4-amplified adipocytic sarcoma as determined by fluorescence in situ hybridization (FISH), or other clinically appropriate methodology in the opinion of the reviewing pathologist. Histologic or imaging evidence of the presence of a dedifferentiated component must be present * Subjects must have one or more measurable target lesions by Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1), assessed via CT scan or MRI * At the time of study enrollment, subjects must have a tumor burden that is judged to be surgically resectable * Have plans to undergo neoadjuvant radiation therapy followed by surgical resection. Review and approval of final treatment plans for subjects receiving radiotherapy locally/at an outside institution must be reviewed and approved by a radiation oncologist investigator prior to initiation of radiotherapy * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (\>= 1.5 GI/L) without granulocyte colony-stimulating factor support in the last 14 days (subjects may not have received blood product transfusion or granulocyte colony-stimulating factor \[G-CSF\] within 14 days prior to screening) * White blood cell count \>= 2500/mm\^3 (\>= 2.5 GI/L) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Platelets \>= 100,000/mm\^3 (\>= 100 GI/L) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Hemoglobin \>= 8 g/dL (\>= 80 g/L) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Alanine aminotransferase (ALT), aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (subjects with Gilbert's disease =\< 2 x ULN and direct bilirubin within normal limits are permitted) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Serum albumin \>= 2.8 g/dl (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Serum creatinine =\< 2.0 x ULN or calculated creatinine clearance \>= 30 mL/min (\>= 0.5 mL/sec) using the Cockcroft-Gault equation (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol) (subjects may not have received blood product transfusion or G-CSF within 14 days prior to screening) * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Male or non-pregnant and non-breast feeding female: * Women of child-bearing potential (WOCBP) must agree to use highly effective contraception without interruption from initiation of therapy and continue until 4 months (120 days) after last dose of study therapy. WOCBP must have a negative serum pregnancy test (beta-human chorionic gonadotropin \[hCG\]) result at screening and agree to ongoing pregnancy testing during the study, and at the end of study treatment. A highly effective method of contraception is defined as one that results in a low failure rate (that is, \< 1% per year), when used consistently and correctly, such as implants, injectables, combined oral contraceptives, some intrauterine contraceptive devices, sexual abstinence, or a vasectomized partner * Male subjects must practice abstinence or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study * Life expectancy of \> 3 months, as determined by the investigator * Ability to understand and sign informed consent * Willingness and ability to comply with scheduled visits, laboratory tests, and other study procedures Exclusion Criteria: * Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy (including investigational) for the investigational diagnosis * Receipt of any prior radiation therapy for any reason to the affected area * Known central nervous system (CNS) metastases * Evidence of distant metastatic disease at time of treatment initiation * History of thromboembolic event within 1 year of treatment initiation. Thromboembolic events include, but are not limited to, deep vein thrombosis, pulmonary embolism, pelvic venous thrombosis, cerebral venous sinus thrombosis, subclavian and axillary vein thrombosis, and inferior vena cava thrombosis * 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 * History of any major surgery within 14 days prior to enrollment * Receipt of ongoing anti-coagulation for treatment or prophylaxis of thromboembolic event in the setting of prior thromboembolic event * History of interstitial lung disease * Subjects with 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) * Pregnant or lactating females * Inability to swallow tablets * Previously identified allergy or hypersensitivity to components of the study treatment formulations * Diagnosis of another malignancy within 2 years before first dose of study treatment, except for superficial skin cancers, or localized tumors deemed cured and not treated with systemic therapy * Concurrent use of medications (especially those interacting with CYP3A) that potentially interact unsafely with abemaciclib which cannot be discontinued or substituted * Recent infection requiring systemic anti-infective treatment that was completed =\< 14 days prior to enrollment (except for uncomplicated urinary tract infection or upper respiratory tract infection). Any 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 for human immunodeficiency virus (HIV)/hepatitis is not required for enrollment * Concurrent enrollment in any other type of medical research (for example: medical device) judged by the investigator not to be scientifically or medically compatible with this study