Cabozantinib S-malate in Treating Patients With Metastatic Pheochromocytomas or Paragangliomas That Cannot Be Removed by Surgery

Inclusion Criteria: * Histological confirmation of pheochromocytoma (PH)/paraganglioma (PG) * Locally advanced or metastatic disease not amenable to surgery * Patients enrolled in the main branch should have measurable disease; patients with a predominance of bone disease who have small, non-measurable or small measurable lesions other than bone, may be included per the principal investigator's discretion, in the exploratory branch of the study for patients with bone metastases only * Progressive disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 as determined by the investigator within the 12 months preceding study enrollment * Assessment of all known disease sites, e.g., by CT scan, MRI, bone scan as appropriate, and/or FDG-PET scan within 28 days before the first dose of cabozantinib * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Life expectancy of at least 3 months * Absolute neutrophil count (ANC) \>= 1500/mm\^3 without colony stimulating factor support (within 4 days prior to the first dose of cabozantinib) * Platelets \>= 100,000/mm\^3 (within 4 days prior to the first dose of cabozantinib) * Hemoglobin \>= 9 g/dL (within 4 days prior to the first dose of cabozantinib) * Bilirubin =\< 1.5 x the upper limit of normal (ULN) (for subjects with known Gilbert's disease, bilirubin =\< 3.0 mg/dL) (within 4 days prior to the first dose of cabozantinib) * Serum albumin \>= 2.8 g/dl (within 4 days prior to the first dose of cabozantinib) * Serum creatinine =\< 1.5 x ULN or creatinine clearance (CrCl) \>= 50 mL/min (for creatinine clearance estimation, the Cockcroft and Gault equation should be used) (within 4 days prior to the first dose of cabozantinib) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3.0 x ULN (within 4 days prior to the first dose of cabozantinib) * Lipase \< 2.0 x ULN and no radiologic or clinical evidence of pancreatitis (within 4 days prior to the first dose of cabozantinib) * Urine protein/creatinine ratio (UPCR) =\< 1 (within 4 days prior to the first dose of cabozantinib) * Serum phosphorus, calcium, potassium \>= lower limit of normal (LLN) (within 4 days prior to the first dose of cabozantinib) * Serum magnesium \>= 1.2 mg/dL (within 4 days prior to the first dose of cabozantinib) * Capable of understanding and complying with the protocol requirements and has signed the informed consent document * Sexually active patients (men and women) must agree to use medically accepted barrier methods of contraception (e.g., male or female condom) during the course of the study and for 4 months after the last dose of study drug(s), even if oral contraceptives are also used; all subjects of reproductive potential must agree to use both a barrier method and a second method of birth control during the course of the study and for 4 months after the last dose of study drug(s) * Women of childbearing potential must have a negative pregnancy test at screening; women of childbearing potential include women who have experienced menarche and who have not undergone successful surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are not postmenopausal; postmenopause is defined as amenorrhea \>= 12 consecutive months; note: women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, antiestrogens, ovarian suppression or any other reversible reason Exclusion Criteria: * Received cytotoxic chemotherapy (including investigational cytotoxic chemotherapy) or biologic agents (e.g., cytokines or antibodies) within 3 weeks, or nitrosoureas/mitomycin C within 6 weeks before the first dose of study treatment * Prior treatment with cabozantinib * Radiation therapy for bone metastasis within 2 weeks, or any other external radiation therapy within 4 weeks before the first dose of study treatment; subjects with clinically relevant ongoing complications from prior radiation therapy are not eligible * Received radionuclide treatment (i.e. iodine \[I\]-131 meta-iodo-benzyl guanidine) within 6 months of the first dose of study treatment * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 14 days before the first dose of study treatment * Receipt of any other type of investigational agent within 28 days before the first dose of study treatment * The subject has not recovered to baseline or CTCAE =\< grade 1 from toxicity due to all prior therapies except alopecia and other non-clinically significant adverse events (AEs) * Prothrombin time (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test \>= 1.3 x the laboratory ULN within 7 days before the first dose of study treatment * The subject requires concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, thrombin or Factor Xa inhibitors, or antiplatelet agents (eg, clopidogrel); low dose aspirin (=\< 81 mg/day), low-dose warfarin (=\< 1 mg/day), and prophylactic low molecular weight heparin (LMWH) are permitted * The subject requires chronic concomitant treatment of strong cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4) inducers (e.g., dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John's wort) * The subject has experienced any of the following: a. clinically-significant gastrointestinal bleeding within 6 months before the first dose of study treatment, b. hemoptysis of \>= 0.5 teaspoon (2.5 ml) of red blood within 3 months before the first dose of study treatment, c. any other signs indicative of pulmonary hemorrhage within 3 months before the first dose of study treatment * Radiographic evidence of cavitating pulmonary lesion(s) * Tumor invading or encasing any major blood vessels * 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 cabozantinib * Uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: a. cardiovascular disorders including: i. congestive heart failure (CHF): New York Heart Association (NYHA) class III (moderate) or class IV (severe) at the time of screening, ii. concurrent uncontrolled hypertension defined as sustained blood pressure \> 150 mm Hg systolic, or \> 90 mm Hg diastolic despite optimal antihypertensive treatment within 7 days of the first dose of study treatment, iii. any history of congenital long QT syndrome, or iv. any of the following within 6 months 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, or thromboembolic event requiring therapeutic anticoagulation (note: subjects 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: i. 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 (patients must be completely recovered), inflammatory bowel disease (including ulcerative colitis and Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis (patient must be completely recovered from these conditions), malabsorption syndrome; ii. any of the following within 6 months before the first dose of study treatment: abdominal fistula, gastrointestinal perforation, bowel obstruction or gastric outlet obstruction, or intra-abdominal abscess (complete resolution of an intra-abdominal abscess must be confirmed prior to initiating treatment with cabozantinib even if the abscess occurred more than 6 months before the first dose of study treatment); c. other disorders associated with a high risk of fistula formation including percutaneous endoscopic gastrostomy (PEG) tube placement within 3 months before the first dose of study therapy, d. other clinically significant disorders such as: i. active infection requiring systemic treatment within 28 days before the first dose of study treatment, ii. serious non-healing wound/ulcer/bone fracture within 28 days before the first dose of study treatment, iii. history of organ transplant, iv. concurrent uncompensated hypothyroidism or thyroid dysfunction within 7 days before the first dose of study treatment, or v. major surgery within 12 weeks before the first dose of study treatment; complete wound healing from major surgery must have occurred 1 month before the first dose of study treatment; minor surgery within 28 days before the first dose of study treatment with complete wound healing at least 10 days before the first dose of study treatment; subjects with clinically relevant ongoing complications from prior surgery are not eligible * Unable to swallow tablets * A corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms within 28 days before first dose of study treatment; three electrocardiograms (ECGs) must be performed; if the average of these three consecutive results for QTcF is =\< 500 msec, the subject meets eligibility in this regard * Pregnant or breastfeeding * A previously identified allergy or hypersensitivity to components of the study treatment formulation * Unable or unwilling to abide by the study protocol or cooperate fully with the investigator or designee * Evidence within 2 years of the start of study treatment of another malignancy which required systemic treatment except for cured nonmelanoma skin cancer or cured in situ cervical carcinoma * Any other severe acute or chronic medical or psychiatric condition or laboratory abnormality which, in the judgment of the investigator, would have made the patient inappropriate for entry into this study