Eribulin Mesylate and Everolimus in Treating Patients With Triple-Negative Metastatic Breast Cancer

Inclusion Criteria: * Patients must have histologically-confirmed stage IV TNBC (patients who had metastatic disease within 6 months of lumpectomy or mastectomy for treatment of TNBC may be excused from repeat biopsy) * Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion; newly obtained is 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 provide (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the study principle investigator (PI) * Patients must have had prior treatment with anthracyclines and/or taxanes (resistant) or platinum including adjuvant or neoadjuvant therapy * Both measurable as well as non-measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1, will be allowed * Patients with chemotherapy for metastatic disease (patients with 0-3 prior lines of chemotherapy for metastatic breast cancer \[MBC\]) * Life expectancy of \>= 3 months * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Hemoglobin \>= 9.0 g/dl * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Creatinine =\< 1.5 times the upper limit of normal (ULN) * Total bilirubin less =\< to 1 times ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< to 2.5 times the ULN if no liver metastases; for patients with known liver metastases, AST and ALT must be =\< to 5 times the ULN * Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for up to 8 weeks after ending treatment; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Be willing to use dexamethasone mouthwash as directed Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events (AEs) due to agents administered \> 3 weeks prior to entering the study * Patients may not be receiving any other investigational agents * Patients with symptomatic brain metastases are excluded from this clinical trial * Uncontrolled current illness including, but not limited to, ongoing or active infection (\> grade 2 based on the National Cancer Institute Common Terminology Criteria for Adverse Events \[NCI CTCAE\] version \[v\]4.0), symptomatic congestive heart failure, unstable angina pectoris, myocardial infarction within the past 6 months, cardiac ventricular arrhythmias requiring anti-arrhythmic therapy, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women * Prior eribulin use * Patients with human immunodeficiency virus (HIV), chronic hepatitis B, or chronic hepatitis C (known from the existing medical record) * Concomitant use with strong or moderate cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4)/P-glycoprotein (PgP) inhibitors and CYP3A4/PgP inducers * Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must use highly effective methods of contraception during the study and 8 weeks after ending treatment; highly effective contraception methods include combination of any two of the following: * Use of oral, injected or implanted hormonal methods of contraception or * Placement of an intrauterine device (IUD) or intrauterine system (IUS) * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Total abstinence * Male/female sterilization Women are considered post-menopausal and not of child-bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g., age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks prior to randomization; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child-bearing potential * Male patients whose sexual partner(s) are WOCBP who are not willing to use adequate contraception, during the study and for 8 weeks after the end of treatment * Noncompliant with oral medication and/or dexamethasone mouth wash