Tivantinib in Treating Patients With Metastatic Prostate Cancer

Inclusion Criteria: * Patients must have histologically documented adenocarcinoma of the prostate with progressive systemic disease (either rising PSA or progression of disease on CT scan or magnetic resonance imaging \[MRI\] or bone scan) despite castrate levels of testosterone due to orchiectomy or luteinizing hormone-releasing hormone (LHRH) agonist or antagonist; castrate levels of testosterone must be maintained throughout the study * Evidence of metastatic disease on CT or bone imaging * Patients must have demonstrated evidence of progressive disease since the most recent change in therapy; progressive disease is defined as any one of the following (measurable disease, bone scan, or PSA progression): * Measurable disease progression: objective evidence of increase \> 20% in the sum of the longest diameters (LD) of target lesions from the time of maximal regression or the appearance of one or more new lesions * Bone scan progression: appearance of two or more new lesions on bone scan attributable to prostate cancer will constitute progression * PSA progression: two successive rises from baseline PSA separated at least by one week with the last value \>= 2 ng/mL * Asymptomatic or minimally symptomatic from prostate cancer - no symptoms attributed to prostate cancer greater than grade I using NCI CTCAE version 4.0 grading of toxicities * Secondary hormonal therapies (e.g., abiraterone acetate, flutamide, estrogen) must be discontinued for at least 4 weeks prior to study enrollment unless the duration of the therapy was less than 8 weeks and there was no demonstrated decrease in PSA * Secondary hormonal therapies with bicalutamide or nilutamide must be discontinued for 6 weeks unless duration of therapy was less than 8 weeks and there was no demonstrated PSA decrease * Prior abiraterone (or investigational anti-androgen) use is allowed; these too will need to be discontinued at least 4 weeks prior to study enrollment * PSA prior to treatment must be \>= 2 ng/ml * Castrate testosterone level (\< 50 ng/dL) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * No prior chemotherapy unless utilized in neoadjuvant/adjuvant setting and must have completed \> 6 months prior to enrollment * Four weeks since major surgery or radiation therapy * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.0 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients must have signed an informed consent document stating that they understand the investigational nature of the proposed treatment * Men and any female partners of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry and for the duration of study participation and for additional 2 months after finishing therapy; should a patient's sexual partner become pregnant or suspect she is pregnant while patient is participating in this study, he should inform the treating physician immediately * Bisphosphonate or denosumab therapy is permitted provided patients began therapy prior to registration and that they continue them as per the manufacturer's guidelines and/or per institutional practice; patients not taking ongoing bisphosphonate or denosumab therapy will not be permitted to start such therapy until they have completed 12 weeks of study treatment * Patients must be able to swallow pills to participate in the study Exclusion Criteria: * Patients who have radiotherapy within 4 weeks or chemotherapy prior to entering the study or those who have not recovered (resolution to grade 1) from adverse events due to agents administered more than 4 weeks earlier; neoadjuvant/adjuvant chemotherapy for local disease is allowed if greater than 6 months have elapsed * Previous hepatocyte growth factor receptor (C-MET) inhibitor treatment (either monoclonal antibody to C-MET or human growth factor \[HGF\] or small molecule inhibitory to C-MET) * History of allergic reactions attributed to compounds of similar chemical or biologic composition ARQ 197 * Caution should be used with patients receiving inhibitors of cytochrome P450 family 2, subfamily C, polypeptide 19 (CYP2C19) and strong inhibitors of cytochrome P450 family 3, subfamily A, polypeptide4 (CYP3A4); additional hematologic testing will be advised if the medication cannot be substituted * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or known psychiatric illness/social situations that would limit compliance with study requirements * Known brain metastasis * Current, recent (within 4 weeks of the first study drug administration), or concurrent planned participation in another investigational therapeutic study * Patients with a "currently active" second malignancy other than non-melanoma skin cancers are not to be registered; patients are not considered to have a "currently active" malignancy if they have completed therapy and are now considered to be at less than 30% risk for relapse (by their physician) * Patients may continue on a daily multi-vitamin and calcium/vitamin D supplements; all other herbal, alternative, and food supplements (i.e., PC-SPES, Saw Palmetto, St. John wort, etc.) must be discontinued before registration * New York Heart Association (NYHA) class III or greater congestive heart failure * History of myocardial infarction or unstable angina within 6 months prior to initial treatment * History of severely impaired lung function * Baseline electrocardiogram (ECG) abnormalities including first degree (PR interval \> 210 ms), second degree, or third degree heart block (exception: patients with pacemakers may be enrolled); QRS prolongation or bundle branch block (QRS \>= 120 ms), or QT prolongation (per institutional standard of care: Fridericia corrected QT interval \[QTcF\] or Bazett corrected QT interval \[QTcB\] \>= 470 ms); other ECG abnormalities will need consideration by the treating investigator and enrollment is up to his/her discretion * Presence of non-healing wound, active ulcer, or untreated bone fracture * Known diabetics that have poorly controlled diabetes mellitus (glycated hemoglobin \[HbA1c\] \>= 8.0%) or fasting glucose level \>= 189 mg/dL (diabetic patient); patients may be potentially eligible once anti-diabetic agent(s) are either added or titrated to control their diabetes mellitus * Active liver disease (AST or ALT \>= 2.0 times the upper limit of normal \[ULN\] or total bilirubin \>= institutional ULN) or gallbladder disease; patients with known liver cirrhosis or severe hepatic impairment (Child-Pugh Class C) will also be excluded * A known history of human immunodeficiency virus (HIV) seropositivity * Impairment of gastrointestinal function or gastrointestinal disease that may significantly alter the absorption of ARQ 197 (e.g., uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or significant small bowel resection) * Patients with an active bleeding diathesis