Inclusion Criteria:

          -  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, unless
             contraindicated

          -  Patients must have progressed on at least one and not more than five prior
             chemotherapy regimens, including in the neoadjuvant, adjuvant, and metastatic settings

          -  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

          -  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) >= 60 mL/min/1.73 m^2

          -  Partial thromboplastin time (PTT) =< 1.5 x ULN

          -  International normalized ratio (INR) =< 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

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiotherapy within 3 weeks

          -  Patients who have had prior treatment with nitrosoureas or mitomycin C

          -  Patients who have had prior treatment with eribulin

          -  Patients who have had prior treatment with PI3K/mTOR/AKT pathway inhibitor

          -  Clinically significant ECG abnormality, including prolonged corrected QT (QTc)
             interval > 480 msec or history of risk factors for Torsades de Pointes (TdP) (i.e.
             congestive heart failure, hypokalemia, hypomagnesemia, bradyarrhythmias, family
             history of long QT syndrome)

          -  Patients with pre-existing neuropathy of grade 2 or higher

          -  Myeloid growth factors within 14 days prior to treatment start

          -  Platelet transfusion within 7 days prior to treatment start

          -  Patients who have not recovered from adverse events due to prior anti-cancer therapy
             (i.e., have residual toxicities > grade 1) with the exception of alopecia

          -  Patients who are receiving any other investigational agents

          -  Immunosuppressive therapy is not allowed while on study

          -  Known tumor AKT mutation from archival tumor tissue analysis

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to copanlisib, PI3K inhibitors, or other agents used in study

          -  Copanlisib is primarily metabolized by CYP3A4. Therefore, the concomitant use of
             strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin,
             ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g.
             rifampin, phenytoin, carbamazepine, phenobarbital, St. John's Wort) are not permitted
             from 14 days prior to enrollment until the end of the study. Other medications that
             are prohibited while on copanlisib treatment:

               -  Herbal medications/preparations (except for vitamins)

               -  Anti-arrhythmic therapy other than beta blockers or digoxin

          -  Systemic corticosteroid therapy at a daily dose higher than 15 mg prednisone or
             equivalent is not permitted while on study. Previous corticosteroid therapy must be
             stopped or reduced to the allowed dose at least 7 days prior to the computed
             tomography/magnetic resonance imaging (CT/MRI) screening. If a patient is on chronic
             corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed
             dose before the screening. Patients may be using topical or inhaled corticosteroids.
             Short-term (up to 7 days) systemic corticosteroids above 15 mg prednisolone or
             equivalent will be allowed for the management of acute conditions (e.g., treatment
             non-infectious pneumonitis). The use of corticosteroids as antiemetics prior to
             copanlisib administration will not be allowed

          -  Patients with uncontrolled intercurrent illness

          -  Patients with psychiatric illness/social situations that would limit compliance with
             study requirements

          -  Patients with non-healing wound, ulcer, or bone fracture

          -  Patients with active, clinically serious infections > grade 2 (Common Terminology
             Criteria for Adverse Events Version 5.0 [CTCAEv5.0]) (viral, bacterial or fungal
             infection)

          -  History of known Pneumocystis jiroveci pneumonia (PJP) infection

          -  Patients with arterial or venous thrombotic or embolic events such as cerebrovascular
             accident (including transient ischemic attacks), deep vein thrombosis or pulmonary
             embolism within 3 months before the start of study medication

          -  Concurrent diagnosis of pheochromocytoma due to risk of hypertension with copanlisib

          -  Uncontrolled hypertension (defined as blood pressure >= 150/90 mm/Hg) despite optimal
             medical management (per investigator's opinion)

          -  Proteinuria as estimated by urine protein/creatinine ratio > 3.5 g/g on random urine
             sample or grade >= 3 as assessed by 24-hour urine protein collection

          -  Patients with history of or current autoimmune disease

          -  Patients with congenital QT prolongation

          -  The patient has a personal history of any of the following conditions: syncope of
             cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but
             not limited to, ventricular tachycardia and ventricular fibrillation), or sudden
             cardiac arrest

          -  Pregnant women are excluded from this study because copanlisib is a PI3K inhibitor
             agent and eribulin is an anti-tubulin agent with the potential for teratogenic or
             abortifacient effects. Because there is an unknown but potential risk for adverse
             events in nursing infants secondary to treatment of the mother with copanlisib and
             eribulin, breastfeeding should be discontinued if the mother is treated with
             copanlisib and/or eribulin. These potential risks may also apply to other agents used
             in this study