Dinaciclib and Epirubicin Hydrochloride in Treating Patients With Metastatic Triple-Negative Breast Cancer

Inclusion Criteria: * Patients must have histologically confirmed estrogen receptor (ER)/progesterone receptor (PR)/human epidermal growth factor receptor 2 (HER2) negative carcinoma of the breast that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective; for purposes of this study, triple negative disease will be tumors that have ER/PR \< 10% and HER2 =\< 1+ by immunohistochemistry (IHC) or HER2 fluorescent in situ hybridization (FISH) non-amplified (ratio \< 2) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Patients must have no more than two prior chemotherapy regimens for metastatic breast cancer; in patients who develop disease recurrence within 6 months of adjuvant or neoadjuvant chemotherapy, the adjuvant or neoadjuvant therapy will be considered one prior regimen for metastatic disease * Life expectancy of greater than 3 months * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal limits unless clinical diagnosis of Gilbert's syndrome * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients must be disease free of prior malignancy for \>= 5 years with the exception of curatively treated squamous cell carcinomas of the skin or carcinoma in situ of the cervix or breast * Must have at least one site of objective measurable or evaluable disease; baseline measurements and evaluations must be obtained within 4 weeks of start of therapy * Patients must have no history of prior therapy with dinaciclib * Concurrent use of hormonal therapy is not permitted; concurrent radiation therapy is not permitted; bisphosphonates are allowed, provided that they were started no less than two weeks prior to initiating protocol therapy * Patients must have completed and recovered from the effects of prior chemotherapy (\< grade 2 toxicity) excluding alopecia * Women of child-bearing potential and men must agree to use adequate contraception (barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of dinaciclib administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events * Patients who are receiving any other investigational agents * Patients with untreated brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition as epirubicin or dinaciclib * Patients receiving any medications or substances that are inhibitors or inducers of cytochrome P450 family 3, subfamily A, polypeptide 4/5 (CYP3A4/5) are ineligible * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with dinaciclib * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Patients who have had prior organ allograft or require immunosuppressive therapy * Patients who have received a cumulative dose of doxorubicin of greater than 360 mg/m\^2 or epirubicin of greater than 600 mg/m\^2; patients who have received \> 240 mg/m\^2 of doxorubicin or \> 400 mg/m\^2 of epirubicin should be advised to undergo evaluation of left ventricular ejection fraction (LVEF) with echocardiogram or multi gated acquisition scan (MUGA) prior to initiating therapy * Patients with a history of New York Heart Association class 3 or 4 heart failure, or history of myocardial infarction, unstable angina or cerebral vascular accident (CVA) within 6 months of protocol registration * LVEF \< 50% by MUGA or echocardiogram (ECHO) * Patients who have history of PR prolongation or atrioventricular (AV) block