• Male or female patients must have metastatic or unresectable carcinoma of the breast that is estrogen receptor (ER) negative (less than 10%), progesterone receptor (PR) negative (less than 10%), and HER2 negative/unamplified

• Patients must have had prior treatment with an anthracycline and taxane in the neoadjuvant, adjuvant, or metastatic setting, unless contraindicated or deemed to be suboptimal therapy per the treating physician

• Patients must have progressed on at least one and not more than five prior chemotherapy regimens, including in the neoadjuvant, adjuvant, and metastatic settings. Prior chemotherapy in the neoadjuvant and/or adjuvant setting counts as one prior line. Prior endocrine therapy, anti-HER2 directed therapies, PARP inhibitors, immunotherapy alone, or other targeted therapy will not count as a prior therapy line, as long as the patient meets the eligibility criteria prior to enrollment. Immunotherapy combined with chemotherapy will be considered one line

• All patients must agree to provide archival tumor material (most recent archival tumor tissue immediately prior to enrollment is strongly preferred) for research and must agree to undergo research tumor biopsy before treatment if presence of easily accessible lesions (judged by the treating physician). For patients with bone only disease, or patients without easily accessible lesions for the baseline research biopsy, availability of archival tumor material (2 x 4-5 micron section unstained slides, plus 15-20 x 10 micron section unstained slides or a tumor rich block) from previous breast cancer diagnosis or treatment is required for PTEN and PIK3CA analysis

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of copanlisib in combination with eribulin in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%)

• Leukocytes \>= 3,000/mcL

• Absolute neutrophil count \>= 1,500/mcL

• Platelets \>= 100,000/mcL

• Hemoglobin \>= 8.0 g/dL

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (=\< 3 x institutional ULN for patients with Gilbert syndrome)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional ULN

• Lipase =\< 1.5 x ULN

• Creatinine \< 1.5 mg/dL AND glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2

• International normalized ratio (INR) =\< 1.5 x ULN

• Partial thromboplastin time (PTT) =\< 1.5 x ULN

• Patients with history of known type I or type II diabetes must have a fasting glucose level of \< 120 mg/dL on at least 2 separate occasions or glycosylated hemoglobin measurement (HbA1c) \< 8.5% at screening within 14 days prior to registration

• Patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to participate provided that their medication dose and INR/PTT is stable

• Prophylactic antiemetics may be administered according to standard practice. The routine use of standard antiemetics, including 5-HT3 blockers, such as granisetron, ondansetron, or an equivalent agent, is allowed as needed, as long as corrected QT (QTc) interval on baseline electrocardiogram (ECG) \< 480 msec. The use of corticosteroids as antiemetics prior to copanlisib administration will not be allowed

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial provided they are on a stable regimen of anti-retroviral therapy (ART) with no medications otherwise prohibited by this protocol (e.g. drug-drug interactions)

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

• Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression. For patients with history of treated brain metastases, brain scans will be performed within 6 weeks of study enrollment. During study enrollment in the phase 2 portion of the study, brain MRI will be performed every 12 weeks or sooner if clinically-indicated in all patients with history of known brain metastases

• For phase 1 portion of the study only: patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy. This is not allowed for phase 2 portion of the study

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better. Patients with history of known congestive heart failure (left ventricular ejection fraction \[LVEF\] \< 50%) must have documented LVEF \>= 50% within 12 months of study enrollment

• Known mutation status for PIK3CA and PTEN from archival tumor tissue analysis

• The effects of copanlisib on the developing human fetus are unknown. For this reason and because maternal toxicity, developmental toxicity and teratogenic effects have been observed in nonclinical studies and PI3K inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation, and for 1 month after the last dose of study medication. 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 3.5 months after completion of study treatment

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible