Study of Abemaciclib in Dedifferentiated Liposarcoma

Inclusion Criteria:

* A diagnosis of dedifferentiated liposarcoma confirmed at MSKCC.
* Metastatic and/or locally advanced or locally recurrent disease that is not surgically resectable.
* All patients must have measurable disease as defined by RECIST 1.1. Patients must also have evidence of disease progression by RECIST 1.1 within 6 months of first dose of study drug.
* Any number of prior therapies (including none) is permitted. The last dose of systemic therapy (include targeted therapies) must have been given at least 2 4 weeks prior to initiation of therapy. Patients receiving BCNU or mitomycin C must have received their last dose of such therapy at least 6 weeks prior to initiation of therapy.
* Patients with brain metastasis that have been treated with definitive surgery or radiation and have been clinically stable for 3 months are eligible.
* Age ≥ 18 years.
* ECOG performance status 0 or 1
* Adequate organ and marrow function as defined below (ULN indicates institutional upper limit of normal):
* Absolute neutrophil count ≥ 1.510\^9/L
* Hemoglobin ≥ 8.0 g/dL
* WBC ≥ 3.0 x 10\^9/L
* Platelets ≥ 100 x 10\^9/L
* Total bilirubin ≤ 1.5 x ULN except for patients with known Gilbert syndrome
* AST(SGOT)/ALT(SGPT) ≤ 3 x institutional ULN
* Creatinine ≤ 1.5 x ULN or Creatinine Clearance \> 50 mL/min (calculated by Cockcroft-Gault method)
* Patients must not have current evidence of another malignancy that requires treatment.
* Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence). Women must not breast feed while on study.
* Ability to understand and the willingness to sign a written informed consent document.
* Ability to swallow capsules

Exclusion Criteria:

* Patients who have not recovered from adverse events of prior therapy to ≤ NCI CTCAEv4.0 Grade 1.
* Patients receiving any other investigational agents.
* Patients who have received prior treatment with a selective CDK4 inhibitor
* Uncontrolled intercurrent illness including, but not limited to, known ongoing or active infection, including HIV, active hepatitis B or C, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia (specifically, atrial fibrillation or ventricular dysrhythmias except ventricular premature contractions), or psychiatric illness/social situations that would limit compliance with study requirements.
* Pregnant women and women who are breast-feeding.