Genetic Analysis in Blood and Tumor Samples From Patients With Advanced or Metastatic Estrogen Receptor Positive and HER2 Negative Breast Cancer Receiving Palbociclib and Endocrine Therapy

Inclusion Criteria: PRE-REGISTRATION INCLUSION CRITERIA * Women who have disease that is amenable to biopsy and agree to undergo a standard of care and /or research biopsy * Note: If a standard of care biopsy was recently obtained =\< 2 months of pre-registration, eligible patients should agree to a research biopsy of recurrent or metastatic breast cancer prior to the start of protocol treatment to collect additional core samples for research purposes * Patients must satisfy one of the following criteria for prior therapy: * First line setting: No prior endocrine therapy in the metastatic setting with no more than one prior line of chemotherapy in the advanced/metastatic setting * Second line setting: Progression on one prior line of endocrine based therapy monotherapy either in the adjuvant or advanced/metastatic setting; either one or two prior lines of chemotherapy in the advanced setting are allowed * Note: Patients receiving bisphosphonate or denosumab therapy prior to registration may continue at the same intervals used prior to study registration * First line therapy setting only: The intention to begin palbociclib and letrozole as treatment for locally advanced or metastatic breast cancer * Second line therapy setting only: The intention to begin palbociclib and fulvestrant as treatment for metastatic breast cancer (after progression on first line endocrine therapy) * Note: Patients who are to receive second line endocrine therapy are allowed to remain on their most recent treatment (tamoxifen or an aromatase inhibitor during the pre-registration period as well as after registration while awaiting insurance approval for the use of palbociclib * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria or bone only disease are eligible. * Note: Those patients with both non-measurable disease and bone metastases are eligible * Note: Patients are not allowed to begin a new systemic anti-cancer therapy during pre-registration with the exception of bisphosphonate or denosumab; palliative radiation to lesions that will not be biopsied or used for assessing disease response (target lesions) is allowed during pre-registration * No current evidence of visceral crisis * History of central nervous system metastasis are allowed provided they have been treated (i.e., surgery, radiation, and/or radiosurgery) \>= 12 weeks prior to pre-registration and have stable neurologic function, including no requirement for medication(s) to control symptoms for at least 2 weeks; Note: patients with known leptomeningeal disease are not eligible * Women who are premenopausal must agree to begin or continue an leutinizing hormone releasing hormone (LHRH) agonist (goserelin preferred) * NOTE: A woman is considered premenopausal if menses has occurred in the last 12 months prior to preregistration and both serum and follicle stimulating hormone (FSH) levels are not in the laboratory's reference range for postmenopausal females * Eastern Cooperative Oncology Group (ECOG) performance status: 0, 1, or 2 * Able to swallow oral formulation of drugs * Signed and dated informed consent document for study participation * Willing to submit tissue, blood, stool, and saliva and urine for required correlative research REGISTRATION INCLUSION CRITERIA * Histologic confirmation from the pre-registration biopsy of either locally advanced or metastatic breast cancer that is ER-positive and HER2 -negative * Note: ER-positive disease is defined as \>= 10% nuclear staining; HER2-negative disease per American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) guidelines, one of the following must apply: * 0 or 1+ by immunohistochemistry (IHC) and not amplified by in situ hybridization (ISH) * 0 or 1+ by IHC and ISH not done * 2+ by IHC and not amplified by ISH or * IHC not done and not amplified by ISH * Absolute neutrophil count (ANC) \>= 1500/mm\^3 (=\< 14 days prior to registration) * Platelet count \>= 100,000/mm\^3 (=\< 14 days prior to registration) * Hemoglobin \>= 9.0 g/dL (=\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN), (=\< 3 x ULN if Gilbert's disease) (=\< 14 days prior to registration) * Aspartate transaminase (AST) =\< 3 x ULN (=\< 5 x ULN if liver metastases present) (=\< 14 days prior to registration) * Creatinine =\< 1.5 x ULN (=\< 14 days prior to registration) * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Toxicities related to all prior anticancer therapies must have resolved or stabilized, apart from alopecia and peripheral neuropathy; Note: Peripheral neuropathy which has resolved to =\< grade 2 toxicity is acceptable Exclusion Criteria: PRE-REGISTRATION EXCLUSION CRITERIA * History of metastatic ER negative or HER2 positive breast cancer * Prior treatment in the metastatic setting with everolimus, or any agent whose mechanism of action is to inhibit the PI3K-mTOR pathway * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Uncontrolled symptomatic cardiac arrhythmia * Uncontrolled hypertension (defined as blood pressure \> 160/90) * Other active second malignancy other than non-melanoma skin cancers =\< 3 years of pre-registration; Note: a second malignancy is not considered active if all treatment for that malignancy is completed and the patient has been disease-free for =\< 3 years prior to pre-registration * Prior hematopoietic stem cell or bone marrow transplantation =\< 3 years of pre-registration * Known hypersensitivity to palbociclib, letrozole, fulvestrant, goserelin (if applicable) or to any of their excipients * Known to be pregnant and planning to continue nursing REGISTRATION EXCLUSION CRITERIA * No tumor identified on biopsy or insufficient tumor cells to obtain ER or HER2 status * Any of the following therapies prior to registration: * Chemotherapy =\< 2 weeks * Immunotherapy =\< 2 weeks * Biologic therapy =\< 2 weeks * Monoclonal antibodies =\< 2 weeks * Note: Denosumab is exempt from this requirement and can be started at any time prior to initiation of palbociclib and letrozole/fulvestrant without the need to delay protocol therapy * Radiation therapy =\< 2 weeks * Note: Palliative radiation therapy to lesions that will not be biopsied for this study or used for assessing disease response (target lesions) is permitted during the pre-registration period and does not count towards the 2 week window * Anti HER2 or other "targeted" therapy =\< 2 weeks * The following patients are not eligible * Pregnant women * Nursing women * Women of childbearing potential who are unwilling to employ adequate contraception * Women who have already commenced treatment with an aromatase inhibitor (first line setting) or fulvestrant (second line setting) prior to screening for this study or any prior palbociclib