Sorafenib in Treating Patients With Regional or Metastatic Cancer of the Urothelium

Inclusion Criteria: * Histologically confirmed transitional cell carcinoma or mixed histologies containing a component of transitional cell carcinoma of the urothelium (renal pelvis, ureter, bladder, urethra) with manifestations of progressing regional or metastatic cancer; or (2) Nontransitional cell histologies include patients with adenocarcinoma or squamous cell carcinomas representing greater than 90% of specimen; patients with small cell carcinoma, soft tissue sarcomas, or carcinosarcomas are excluded * Measurable disease, as defined in the RECIST criteria; all sites of disease must be evaluated within 4 weeks prior to registration * Patients must have progressed on one and only one prior systemic chemotherapy for metastatic disease; prior chemotherapy administered in the adjuvant or neoadjuvant setting is permitted (i.e. does not count as 1 prior regimen) provided that it was completed greater than 12 months prior to the start of the first chemotherapy regimen administered in the metastatic setting * Patients must not have had prior systemic biologic response modifier therapy; patients must not have had chemotherapy, hormonal or biologic therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or have recovered from adverse events due to agents administered more than 4 weeks earlier * Prior radiotherapy is allowed; patients must be \>= 2 weeks post-radiotherapy at time of registration; a previously irradiated lesion can only be used as a marker lesion if there is unequivocal evidence of progression demonstrated on serial imaging studies; patients must have recovered from all toxicities associated with prior radiotherapy * Patients must be \>= 4 weeks post-major surgery at time of registration; patients must have recovered from all toxicities associated with prior surgery * ECOG performance status of 0 or 1 * No history of severe cardiovascular disease (AHA Class III or IV), uncontrolled CHF, uncontrolled hypertension, or ventricular dysrhythmias * Patients with previously resected and irradiated CNS metastases with evidence of stable disease are eligible * Patients with a history of prior malignancy are eligible provided they were treated with curative intent and have been disease free for \>= 5 years; curatively treated basal cell or squamous cell carcinoma of the skin or carcinoma-in-situ of the cervix must have been treated with curative intent; patients with clinically unsuspected organ confined prostate cancer found at the time of cystoprostatectomy are eligible * Creatinine \< 1.5 mg/dL * Granulocytes \>= 1500/mm\^3 * Platelets \>= 100,000/mm\^3 * AST =\< 2.5 x institutional upper limit of normal * Bilirubin \< 1.5 mg/dl * No active unresolved infection requiring parenteral antibiotics \< 7 days prior to study entry * Patients must not have a swallowing dysfunction which would prevent the ingesting of pills * Patients must not have any evidence of bleeding diathesis * Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (i.e. low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for PT, INR or PTT are met * Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, and phenobarbital), rifampin, or St. John's Wort * Women of childbearing potential must not be pregnant (as proven by a negative pregnancy test within 14 days prior to registration) or breast feeding because the effects of this treatment on the fetus and breast-fed infants is unknown * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception