Inclusion Criteria:

- Age ≥ 18 years

- Histologically confirmed diagnosis of dedifferentiated liposarcoma which is locally
recurrent and/or metastatic. This study will accept the diagnosis made at the
investigator's center.

- ECOG Performance Status of 0 or 1.

- At least one site of measurable disease on CT/MRI scan as defined by RECIST 1.1
criteria. Baseline imaging must be performed within 28 days of Day 1 of study.

- Adequate organ function

- The patient can swallow oral medications.

- 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 randomization.

- 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 randomization. A washout
period of at least 21 days is required between last chemotherapy dose and
randomization (provided the patient did not receive radiotherapy).

- Written, voluntary informed consent

- Fertile men and women of childbearing potential must agree to use a highly effective
method of birth control during the treatment period and for 3 weeks after last study
drug administration in both sexes. Women of childbearing potential include
pre-menopausal women and women within the first 2 years of the onset of menopause.
Women of childbearing potential must have a negative pregnancy test ≤ seven days of
the first dose of abemaciclib.

- Highly effective methods of birth control include an intrauterine device [IUD] or
barrier method. If condoms are used as a barrier method, a spermicidal agent should be
added as a double barrier protection.

- Measurable disease and evidence of progression of disease as defined by RECIST 1.1
(including newly diagnosed disease, new disease sites in a patient who was previously
NED, or a 20% growth of existing lesions within 6 months of registration).

- Patients with central nervous system disease are eligible for enrollment if they have
received prior radiotherapy or surgery within 3 months from completion of therapy to
sites of CNS metastatic disease and are without evidence of clinical progression.

Exclusion Criteria:

- Patients with documentation of well-differentiated liposarcoma only are specifically
excluded, owing to its characteristically slow growth. If high grade areas are
suspected (dedifferentiation), but not proved by pathology analysis (e.g. after
primary resection of a well-differentiated liposarcoma), a biopsy must be performed to
demonstrate the high-grade dedifferentiated disease. If there is a question regarding
the diagnosis, the PI should be consulted.

- Patients with bulky disease who urgently need cytotoxic chemotherapy (likely with
doxorubicin + ifosfamide) will be excluded from this study. This is determined by the
treating physician. If there is a question regarding the appropriateness of the
patient for enrollment, the PI should be consulted.

- Prior systemic therapy with abemaciclib or any other selective CDK4 inhibitor (such as
palbociclib)

- Concurrent, clinically significant, active malignancies within 12 months of study
enrollment

- Patients with severe and/or uncontrolled concurrent medical disease that in the
opinion of the investigator could cause unacceptable safety risks or compromise
compliance with the protocol

- Major surgery within 3 weeks prior to Day 1 of study or who have not recovered
adequately from prior surgery

- Patients with resectable for curative intent disease

- Patients that have GI absorption disorders that would impact the administration of
oral abemaciclib.

- Women who are pregnant or nursing/breastfeeding.

- Known hypersensitivity to abemaciclib.

- Patients with untreated central nervous system disease.

- Inability to comply with protocol required procedures

- Patients currently taking the following drugs may interact with abemaciclib. Please
refer to Section 5.2 of protocol.

- 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).

- 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.

- 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.

- The patient has received an experimental treatment in a clinical trial within the last
30 days or 5 half-lives, whichever is longer, prior to randomization, or is currently
enrolled in any other type of medical research (for example: medical device) judged by
the sponsor not to be scientifically or medically compatible with this study.

Note: Other protocol defined Inclusion/Exclusion criteria may apply.

Eligibility last updated 9/15/22. Questions regarding updates should be directed to the study team contact.