Pembrolizumab and Doxorubicin Hydrochloride or Anti-Estrogen Therapy in Treating Patients With Triple-Negative or Hormone Receptor-Positive Metastatic Breast Cancer

Inclusion Criteria: * Patients with 1) stage IV metastatic triple negative breast cancer (triple negative is defined as estrogen receptor \[ER\] and progesterone receptor \[PgR\] status is \< 1% of tumor cell nuclei are immunoreactive for ER or PgR, and HER2 status is fluorescence in situ hybridization \[FISH\] negative or immunohistochemistry \[IHC\] 0 or 1+), or 2) stage IV HR+ HER2- (HR+) breast cancer (defined as ER or PgR \> 1% of tumor cell nuclei are immunoreactive for ER or PgR and HER2 statis is FISH negative or IHC - or 1+) * Be willing and able to provide written informed consent/assent for the trial * Have measurable disease based on RECIST 1.1 * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; newly-obtained in defined as a specimen obtained up to 6 weeks (42 days) prior to initiation of treatment on day 1; subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the sponsor * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) * Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]); creatinine clearance should be calculated per institutional standard * Left ventricular ejection fraction by multigated acquisition scan (MUGA) or echocardiogram \>= 55% for patients with triple negative breast cancer; \>= upper limit of institutional normal for patient with HR+ breast cancer * Serum total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with liver metastases * Albumin \>= 2.5 mg/dL * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Reproductive status for cohort 2: HR+ stage IV post-menopausal breast cancer; post-menopausal is defined by at least one of the following criteria: * Prior bilateral oophorectomy OR amenorrheic for \>= 12 months (if =\< 55 years of age and prior chemotherapy or on medical ovarian ablative therapy or received ovarian radiation for ablation in the past 5 years and/or tamoxifen or an aromatase inhibitor (AI) within the past year, then follicle-stimulating hormone (FSH) and estradiol must be in the post-menopausal range and obtained within 28 days prior to registration) OR * Previous hysterectomy with one or both ovaries left in place (or previous hysterectomy in which documentation of bilateral oophorectomy is unavailable AND FSH values consistent with the institutional normal values for the post-menopausal state; FSH levels must be obtained within 28 days prior to registration * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Subjects currently on a bisphosphonate or denosumab are eligible for study therapy Exclusion Criteria: * Cohort 1: Has triple negative breast cancer, is considered for cohort 1 participation, and received prior anthracycline therapy * Cohort 2: Has received prior aromatase inhibitor therapy and is deemed to be resistant to all three (anastrozole, letrozole, exemestane) approved AIs; resistance is defined as progression within 12 months or while on an AI * Patient is premenopausal (medical ovarian suppression is allowed); is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has a known history of active TB (Bacillus tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients * Suboptimal cardiac function as defined by decreased left ventricular ejection fraction \< 55% for cohort 1, and \< 50% for cohort 2 * Prior pembrolizumab * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study; Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that has progressed or required active treatment in the past 5 years; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of, active pneumonitis requiring treatment with steroids or history of/active interstitial lung disease * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-programmed death-ligand (PD-L)1, or anti-PD-L2 agent * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has a history of (non-infectious) pneumonitis that required steroids or currently has pneumonitis * Has received a live vaccine within 30 days of planned start of study therapy; Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed