Tivantinib in Treating Patients With Previously Treated Malignant Mesothelioma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed malignant pleural or peritoneal mesothelioma, epithelial, sarcomatoid, or mixed subtype; the patient's disease must be metastatic, recurrent, or unresectable * Patients 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, magnetic resonance imaging (MRI), or calipers by clinical exam; pleural effusions and ascites are not considered measurable lesions * No more than two prior cytotoxic chemotherapy regimens; prior chemotherapy with pemetrexed is required; prior intrapleural cytotoxic agents (including bleomycin) are allowed, and are not counted as a cytotoxic chemotherapy; chemotherapy must have been completed at least 4 weeks prior; patients who have previously received radiation therapy are eligible provided that the only site of measurable disease is not located within the radiation therapy port; at least 4 weeks must have elapsed from completion of the radiation therapy and all signs of toxicity must have resolved * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Life expectancy of greater than 3 months * Hemoglobin \>= 9.0 g/dL * White blood cells (WBC) \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 X institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Serum creatinine =\< 1.5 X institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * The effects of ARQ 197 on the developing human fetus are unknown; for this reason and because tyrosine kinase inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men 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; 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 4 months after completion of ARQ 197 administration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events (to grade =\< 1) due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ARQ 197 * ARQ 197 is metabolized by cytochrome P450 (CYP)2C19, and to a lesser extent CYP3A4; the metabolism and consequently overall pharmacokinetics of ARQ 197 could be altered by inhibitors and/or inducers or other substrates of CYP2C19 and CYP3A4; while inhibitors/inducers of these cytochrome P450 isoenzymes are not specifically excluded, investigators should be aware that ARQ 197 exposure may be altered by the concomitant administration of these drugs; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * 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 because ARQ 197 is a tyrosine kinase inhibitor 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 ARQ 197, breastfeeding should be discontinued if the mother is treated with ARQ 197 * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with ARQ197; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated * No prior treatment with a c-MET inhibitor