Tivantinib in Treating Patients With Recurrent or Metastatic Breast Cancer

Inclusion Criteria:

* Participants must have histologically or cytologically confirmed invasive breast cancer, with recurrent or metastatic disease; participants without pathologic or cytologic confirmation of metastatic disease should have unequivocal evidence of metastasis from physical examination or radiologic evaluation
* Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan
* Participants must have recent evidence of progressive disease

  * Participants must have received 1-3 prior chemotherapeutic regimens for metastatic breast cancer and must have been off treatment with chemotherapy for at least 14 days before enrollment in the study
* Participants must have discontinued all biologic therapy (including vaccines) at least 14 days before enrollment in the study
* Participants must have discontinued any investigational therapy at least 14 days before enrollment in the study
* Participants may have received prior radiation therapy in either the metastatic or early-stage setting

  * Radiation therapy must be completed at least 14 days before enrollment in the study
  * Participant must not have received radiation to \> 25% of his or her bone marrow within 30 days of starting study treatment
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Hemoglobin \>= 9.0 g/dL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin =\< 1.5 times upper limit of normal (ULN)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 times institutional ULN; for participants with documented liver metastases, AST/ALT =\< 5.0 times ULN
* Serum creatinine =\< 1.5 times ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for participants with creatinine levels above institutional normal
* Either the primary tumor and/or the metastasis must be triple-negative; the invasive tumor must be hormone-receptor poor, defined as estrogen-receptor negative (ER-) and progesterone-receptor negative (PR-), or staining \< 10% by immunohistochemistry (IHC)

  * Human epidermal growth factor receptor 2 (HER2) status: the invasive tumor must be HER2-negative, defined as 0 or 1+ by IHC, or FISH \< 2.0
* Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) during the study and for 90 days after the last investigational drug dose received
* Female subjects of childbearing potential must have a negative serum pregnancy test within 21 days of cycle 1 day 1
* Participants on bisphosphonates may continue receiving bisphosphonate therapy during study treatment; bisphosphonate therapy may also be initiated on study treatment if needed
* Confirmed availability of formalin-fixed, paraffin-embedded (FFPE) tumor tissue
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Participants who have received chemotherapy, biologic, investigational, or radiotherapy within 14 days prior to entering the study
* Participants who are receiving any other investigational agents
* Known brain metastases that are untreated, symptomatic, or require therapy to control symptoms

  * Participants with a history of treated central nervous system (CNS) metastases are eligible

    * Treated brain metastases are defined as those having no evidence of progression or hemorrhage for \>= 2 months after treatment, and no ongoing requirement for corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging or computed tomography \[CT\] scan) during the screening period
    * Treatment for brain metastases may include whole-brain radiotherapy, radiosurgery, or a combination as deemed appropriate by the treating physician
  * Participants may be taking anti-convulsant medications, which must be non-enzyme-inducing anti-epileptic drugs
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to ARQ 197
* History of congestive heart failure defined as Class II to IV per New York Heart Association (NYHA) classification; active coronary artery disease (CAD); clinically significant bradycardia or other uncontrolled, cardiac arrhythmia defined as \>= grade 3 according to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0, or uncontrolled hypertension; myocardial infarction occurring within 6 months prior to study entry (myocardial infarction occurring \> 6 months prior to study entry is permitted)
* 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
* Human immunodeficiency virus (HIV)-positive participants on combination antiretroviral therapy are ineligible