A Phase II Trial to Evaluate Functional Imaging in Prediction of Response to Abemaciclib for Advanced Hormone Receptor-Positive, HER2-Negative Breast Cancer

Inclusion Criteria: * Men or women with metastatic or locally advanced unresectable breast cancer * Histologically confirmed ER+ / HER2-negative, breast cancer who is a candidate for endocrine therapy with pathology from the primary tumor or metastatic/recurrent site. Based on American Society of Clinical Oncology/College of American Pathologists (ASCO CAP) Guidelines: ER+: \>= 1% of tumor cell nuclei to be immunoreactive. HER2-negative: HER2 of 0, 1+ by immunohistochemistry (IHC) or negative by fluorescence in situ hybridization (FISH). * In the case of bone biopsy which could yield false negative ER or PR status in patients with historically HR+ disease, a patient may be eligible if the treating physician and the study chair both agree that the patient is a candidate for further endocrine therapy (ET) based treatment. * Note that baseline PR status by IHC does not influence results of deltaFFNP-PET imaging. * If premenopausal, the patient has to be treated with GnRH agonist for at least 6 weeks prior to FFNP-PET. * Disease must be present in at least one non-liver site and measurable by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria and be 1.5 cm or greater in longest dimension OR disease can be non-measurable but must be 1.5 cm in longest dimension on functional imaging (fluorodeoxyglucose \[FDG\]-PET/computed tomography \[CT\] preferred). * No limits to prior lines of endocrine therapy in the metastatic setting including synergistic targeted therapy such as CDK4/6 inhibitors (other than Abemaciclib), PI3K inhibitor, mTOR inhibitor, etc. One line of prior cytotoxic chemotherapy in the metastatic setting is allowed. Washout from prior systemic anti-cancer therapy of at least 2 weeks from chemotherapy or radiation, 2 weeks or 5 half lives (whichever is longer) from oral selective estrogen receptor degrader (SERD), 8 weeks from oral selective estrogen receptor modulator (SERM), and 16 weeks from intramuscular SERD (Fulvestrant) is required. Recovery of adverse events from the last therapy to grade 1 except alopecia. Patients may continue luteinizing hormone-releasing hormone (LHRH) agonist to remain post-menopausal without a need for washout * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * At least 18 years of age * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Hemoglobin \>= 9g/dL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN). * In case of known Gilbert's syndrome, \< 2 x ULN is allowed * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT) /alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) =\< 2.5x institutional ULN, or =\< 5 x ULN for subjects with documented metastatic disease to the liver * eGFR (estimated glomerular filtration rate) ≥ 30 mL/min * Women of childbearing potential must agree to use adequate contraception (barrier method of birth control, abstinence) prior to study entry and for the duration of study participation * Ability to understand and willingness to sign an institutional review board (IRB)-approved written informed consent document (or that of legally authorizes representative, if applicable) * Consent to access archival tumor specimens for clinical sequencing data of tumor tissue and blood Exclusion Criteria: * Prior abemaciclib in the metastatic setting or within 2 years of completion of adjuvant abemaciclib * Hepatic-only metastatic disease * A history of other malignancy with the exception of malignancies for which all treatment was completed at least 2 years before registration and the patient has no evidence of disease * Currently receiving any other investigational agents * Untreated/unstable brain metastases. Patients with treated/stable brain metastases, defines as patients who have received prior therapy for their brain metastases and whose central nervous system (CNS) disease is radiographically stable at study entry, are eligible * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to FFNP, abemaciclib, or other agents used in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia * Pregnant and/or breastfeeding women of childbearing potential must have a negative pregnancy test within 14 days of study entry. Male participants and female participants of childbearing potential must utilize adequate contraceptive methods throughout study treatment and for at least 30 days after the last dose of study medications * Patients with human immunodeficiency virus (HIV) are eligible unless their CD4+ T-cell counts are \< 350 cells/mcL or they have a history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infection within the 12 months prior to registration. Concurrent treatment with effective antiretroviral therapy (ART) according to Department of Health and Human Services (DHHS) treatment guidelines is recommended