Cabozantinib and Enfortumab Vedotin for Urothelial Cancer

Inclusion Criteria: * Histologically-documented urothelial carcinoma (squamous differentiation or mixed cell types allowed if urothelial carcinoma is present) * Metastatic disease or unresectable locally-advanced disease * Must have received prior treatment with a checkpoint inhibitor (CPI). A CPI is defined as a programmed cell death protein 1 (PD-1) or programmed death-ligand 1 (PD-L1) inhibitor alone or with any other combination * Must either have prior treatment with platinum-containing chemotherapy or be ineligible at time of enrollment * Recovery to baseline or =\< grade 1 Common Terminology Criteria for Adverse Events (CTCAE) v5.0 from toxicities related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy * Tumor tissue samples must be available for submission prior to initiation of study treatment or patient must be willing to undergo repeat tumor biopsy * Must have measurable disease according to Response Evaluation Criteria in Solid Tumors (RECIST) (Version 1.1) * An Eastern Cooperative Oncology Group (ECOG) performance status score of =\< 2 * Must be \>= 18 years of age * Absolute neutrophil count (ANC) \>= 1500/uL without granulocyte colony-stimulating factor support (within 28 days before first dose of study treatment) * White blood cell count \>= 2500/uL (within 28 days before first dose of study treatment) * Platelets \>= 100,000/uL without transfusion (within 28 days before first dose of study treatment) * Hemoglobin \>= 9 g/dL (within 28 days before first dose of study treatment) * Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) =\< 3 x upper limit of normal (ULN). ALP =\< 5 x ULN with documented bone metastases (within 28 days before first dose of study treatment) * Total bilirubin =\< 1.5 x ULN (for subjects with Gilbert's disease =\< 3 x ULN) (within 28 days before first dose of study treatment) * Prothrombin (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test \< 1.3 x the laboratory ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants (within 28 days before first dose of study treatment) * Calculated creatinine clearance \>= 30 mL/min (\>= 0.5 mL/sec) using the Cockcroft-Gault equation (within 28 days before first dose of study treatment) * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol), or 24-hour (h) urine protein =\< 1 g (within 28 days before first dose of study treatment) * Capable of understanding and complying with the protocol requirements and must have signed the informed consent document * Sexually active fertile subjects and their partners must agree to use medically accepted methods of contraception (e.g., barrier methods, including male condom, female condom, or diaphragm with spermicidal gel) during the course of the study and for 4 months after the last dose of study treatment * Female subjects of childbearing potential must not be pregnant at screening. Female subjects are considered to be of childbearing potential unless one of the following criteria are met: documented permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes. In addition, females \< 55 years-of-age must have a serum follicle stimulating (FSH) level \> 40 mIU/mL to confirm menopause). Note: Documentation may include review of medical records, medical examinations, or medical history interview by study site Exclusion Criteria: * Prior treatment with cabozantinib * Prior enrollment in an enfortumab vedotin study or prior treatment with other monomethyl auristatin E (MMAE)-based antibody-drug conjugates (ADCs) * Receipt of any type of small molecule kinase inhibitor (including investigational kinase inhibitor) within 2 weeks before first dose of study treatment * Receipt of any type of cytotoxic, biologic or other systemic anticancer therapy (including investigational) within 2 weeks before first dose of study treatment * Radiation therapy within 2 weeks before first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before first dose of study treatment * Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks prior to first dose of study treatment after radiotherapy or at least 4 weeks prior to first dose of study treatment after major surgery (e.g., removal or biopsy of brain metastasis). Subjects must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Eligible subjects must be neurologically asymptomatic and without corticosteroid treatment at the time of first dose of study treatment * Concomitant anticoagulation with coumarin agents (e.g., warfarin), direct thrombin inhibitors (e.g., dabigatran), direct factor Xa inhibitor betrixaban, or platelet inhibitors (e.g., clopidogrel). Allowed anticoagulants are the following: * Prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH). * Therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, or apixaban in subjects without known brain metastases who are on a stable dose of the anticoagulant for at least 1 week before first dose of study treatment without clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias. * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 140 mm Hg systolic or \> 90 mm Hg diastolic despite optimal antihypertensive treatment. * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (e.g., deep venous thrombosis, pulmonary embolism) within 6 months before first dose of study treatment * Subjects with a diagnosis of incidental, subsegmental pulmonary embolism (PE) or deep venous thrombosis (DVT) within 6 months are allowed if stable, asymptomatic, and treated with a stable dose of permitted anticoagulation for at least 1 week before first dose of study treatment * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * The subject has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (e.g., Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction. * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose of study treatment. * Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose of study treatment * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (e.g., pulmonary hemorrhage) within 12 weeks before first dose of study treatment * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation * Lesions invading or encasing any major blood vessels * Ongoing sensory or motor neuropathy grade \>= 2 * Other clinically significant disorders that would preclude safe study participation. * Serious non-healing wound/ulcer/bone fracture. * Uncompensated/symptomatic hypothyroidism. * Moderate to severe hepatic impairment (Child-Pugh B or C). * Uncontrolled diabetes mellitus defined as a hemoglobin A1C \>= 8% * Major surgery (e.g., laparoscopic nephrectomy, GI surgery, removal or biopsy of brain metastasis) within 2 weeks before first dose of study treatment. Minor surgeries within 10 days before first dose of study treatment. Subjects must have complete wound healing from major surgery or minor surgery before first dose of study treatment. Subjects with clinically relevant ongoing complications from prior surgery are not eligible * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms per electrocardiogram (ECG) within 14 days before first dose of study treatment. Note: If a single ECG shows a QTcF with an absolute value \> 500 ms, two additional ECGs at intervals of approximately 3 min must be performed within 30 min after the initial ECG, and the average of these three consecutive results for QTcF will be used to determine eligibility * Pregnant or lactating females * Inability to swallow tablets * Previously identified allergy or hypersensitivity to components of the study treatment formulations * Any other active malignancy at time of first dose of study treatment or diagnosis of another malignancy within 3 years prior to first dose of study treatment that requires active treatment, except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or prostate, cervix, or breast