Cabozantinib-S-Malate Compared With Temozolomide or Dacarbazine in Treating Patients With Metastatic Melanoma of the Eye That Cannot Be Removed by Surgery

Inclusion Criteria: * Histologically or cytologically confirmed uveal melanoma that is metastatic or unresectable; if histologic or cytologic confirmation of the primary is not available, confirmation of the primary diagnosis of uveal melanoma by the treating investigator can be clinically obtained, as per standard practice for uveal melanoma; pathologic confirmation of diagnosis will be performed at the participating site * 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 or magnetic resonance imaging (MRI) * Prior systemic therapies allowed, except for those treatments directed toward, or with activity against, c-Met or vascular endothelial growth factor/receptor (VEGF/R), and the chemotherapy agents temozolomide and dacarbazine; prior treatment must have been no earlier than 3 weeks prior to starting treatment with cabozantinib with exceptions noted below and the following: at least 4 weeks since prior hepatic infusion or at least 2 weeks since radiation therapy * No cytotoxic chemotherapy including investigational cytotoxic chemotherapy or biologic agents (e.g., cytokines or antibodies) within the last 3 weeks, or nitrosoureas/mitomycin C within 6 weeks before the first dose of study treatment; at least 6 weeks must have elapsed if the last regimen included an anti-cytotoxic T-lymphocyte antigen 4 (CTLA4) antibody; patients must have experienced disease progression on their prior therapy in the opinion of the treating investigator * No prior radiation therapy within the last 4 weeks, except as below * To the thoracic cavity, abdomen, or pelvis within 12 weeks before the first dose of study treatment, or has ongoing complications, or is without complete recovery to \< grade 1 toxicity * To bone or brain metastasis within 14 days before the first dose of study treatment * To any other site(s) within 28 days before the first dose of study treatment * Prior radiation treatment may have included no more than 3000 centigray (cGy) to fields including substantial bone marrow * No prior radionuclide treatment within 6 weeks of the first dose of study treatment * No prior treatment with a small molecule kinase inhibitor or a hormonal therapy within 14 days or 5 half-lives (whichever is longer) * No concomitant anti-cancer therapy unless specified above * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * A corrected QT interval calculated by the Fridericia formula (QTcF) =\< 500 ms within 28 days before randomization; Note: if initial QTcF is found to be \> 500 ms, two additional electrocardiograms (EKGs) separated by at least 3 minutes should be performed; if the average of these three consecutive results for QTcF is =\< 500 ms, the patient meets eligibility in this regard * Common Terminology Criteria for Adverse Events (CTCAE) recovered to baseline or CTCAE =\< grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant adverse events (AEs) * No active brain metastases or epidural disease; patients with brain metastases previously treated with whole brain radiation or radiosurgery or patients with epidural disease previously treated with radiation or surgery who are asymptomatic and do not require steroid treatment for at least 2 weeks before starting study treatment are eligible; neurosurgical resection of brain metastases or brain biopsy is permitted if completed at least 12 weeks before starting study treatment; baseline brain imaging with contrast-enhanced CT or MRI scans for patients with known brain metastases is required to confirm eligibility * No clinically significant gastrointestinal bleeding within 24 weeks before the first dose of study treatment * No hemoptysis of \>= 0.5 teaspoon (2.5 mL) of red blood within 12 weeks before the first dose of study treatment * No signs indicative of pulmonary hemorrhage within 12 weeks before the first dose of study treatment * No prior radiographic evidence of cavitating pulmonary lesion(s) * No tumor in contact with, invading or encasing any major blood vessels * No evidence of tumor invading the gastrointestinal (GI) tract (esophagus, stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or endobronchial tumor within 28 days before the first dose of treatment * The patient may not have uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders including: * Congestive heart failure (CHF): New York Heart Association (NYHA) class III (moderate) or class IV (severe) at the time of screening * Concurrent uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mmHg systolic, or \> 90 mmHg diastolic despite optimal antihypertensive treatment within 7 days of the first dose of study treatment * Any history of congenital long QT syndrome * Any of the following within 24 weeks before the first dose of study treatment: * Unstable angina pectoris * Clinically-significant cardiac arrhythmias * Stroke (including transient ischemic attack \[TIA\], or other ischemic event) * Myocardial infarction * Thromboembolic event requiring therapeutic anticoagulation (Note: patients with a venous filter \[e.g. vena cava filter\] are not eligible for this study) * Gastrointestinal disorders particularly those associated with a high risk of perforation or fistula formation including: * Any of the following within 28 days before the first dose of study treatment * Intra-abdominal tumor/metastases invading GI mucosa * Active peptic ulcer disease * Inflammatory bowel disease (including ulcerative colitis and Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis * Malabsorption syndrome * Any of the following within 24 weeks before the first dose of study treatment: * Abdominal fistula * Gastrointestinal perforation * Intra-abdominal abscess; Note: complete resolution of an intra-abdominal abscess must be confirmed prior to initiating treatment with cabozantinib even if the abscess occurred more that 24 weeks before the first dose of study treatment * Bowel obstruction or gastric outlet obstruction * Other clinically significant disorders such as: * Serious non-healing wound/ulcer/bone fracture within 28 days before the first dose of study treatment * History of organ transplant * Concurrent uncompensated hypothyroidism or thyroid dysfunction within 7 days before the first dose of study treatment * History of major surgery as follows: * Major surgery in past 8 weeks of the first dose of cabozantinib if there were no wound healing complications or within 24 weeks of the first dose of cabozantinib if there were wound complications * Minor surgery within 4 weeks of the first dose of cabozantinib if there were no wound healing complications or within 12 weeks of the first dose of cabozantinib if there were wound complications * In addition, complete wound healing from prior surgery must be confirmed at least 28 days before the first dose of cabozantinib irrespective of the time from surgery * Active infection requiring systemic treatment within 28 days before the first dose of study treatment * No concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, thrombin or factor Xa inhibitors, or antiplatelet agents (e.g., clopidogrel); low dose aspirin (=\< 81 mg/day), low-dose warfarin (=\< 1 mg/day), and prophylactic low molecular weight heparin (LMWH) are permitted; please note that drugs that strongly induce or inhibit cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) or are associated with a risk of Torsades are not allowed; chronic concomitant treatment of CYP3A4 inducers is not allowed (e.g., dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John's wort); 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; the following drugs are strong inhibitors of CYP3A4 and are not allowed during the treatment with cabozantinib: * Boceprevir * Indinavir * Nelfinavir * Lopinavir/ritonavir * Saquinavir * Telaprevir * Ritonavir * Clarithromycin * Conivaptan * Itraconazole * Ketoconazole * Mibefradil * Nefazodone * Posaconazole * Voriconazole * Telithromycin * Drugs with possible or conditional risk of torsades should be used with caution knowing that cabozantinib could prolong the QT interval * Patients who are pregnant or nursing are not eligible; women of child bearing potential must have a negative serum or urine pregnancy test within 16 days prior to registration; women of child-bearing potential include: * Any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is not postmenopausal (defined as amenorrhea \>= 12 consecutive months) * Women on hormone replacement therapy (HRT) with documented serum follicle stimulating hormone (FSH) level \> 35m IU/mL * Women who are using oral, implanted or injectable contraceptive hormones or mechanical products such as an intrauterine device or barrier methods (diaphragm, condoms, spermicides) to prevent pregnancy or practicing abstinence or where partner is sterile (e.g., vasectomy) * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to cabozantinib, temozolomide and dacarbazine * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 × upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5.0 × institutional upper limit of normal (for patients with metastases); AST (SGOT)/ALT (SGPT) =\< 2.5 × institutional upper limit of normal (for patients without metastases) * Serum creatinine =\< 1.5 × ULN, OR calculated creatinine clearance \>= 30 mL/minute (modified Cockcroft and Gault formula) * Hemoglobin \>= 9 g/dL * Serum albumin \>= 2.8 g/dL * Urine protein/creatinine ratio (UPCR) =\< 1; if urine/protein creatinine (UPC) \>= 1, then a 24-hour urine protein must be assessed; eligible patients must have a 24-hour urine protein value \< 1 g/L * Thyroid-stimulating hormone (TSH) within normal limits (WNL); supplementation is acceptable to achieve a TSH WNL; in patients with abnormal TSH however free T4 and free thyroxine index (FTI) are normal and patient is clinically euthyroid, patient is eligible * Prothrombin time (PT)/international normalized ratio (INR) must be =\< 1.2 x the laboratory ULN * No clinical or radiographic evidence of pancreatitis