Sunitinib Malate or Sorafenib Tosylate in Treating Patients With Kidney Cancer That Was Removed By Surgery

Inclusion Criteria:

* Pre-surgical criteria:

  * Patients must have primary-intact renal cell carcinoma, eligible for nephrectomy with curative intent
  * Tumors \>= 4 cm AND/OR macroscopic fully resectable nodes AND/OR surgically resectable renal vein thrombus AND/OR surgically resectable inferior vena caval thrombus by radiologic criteria to be clinically \>= pT1bNany (resectable) M0 disease
  * Multifocal ipsilateral renal cell carcinoma is allowed provided fully resectable and does not exceed inclusion criteria
* Patients must have no history of distant metastases
* No prior anti-cancer therapy for renal cell carcinoma is permitted in either the adjuvant or neoadjuvant setting; this includes metastectomy for renal cell carcinoma, or radiation therapy to the renal bed
* Patients must not have other current malignancies, other than basal cell skin cancer, squamous cell skin cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the breast; patients with other malignancies are eligible if they have been continuously disease-free for \>= 5 years prior to the time of registration
* Patients must have no serious intercurrent illness including, but not limited to, the following: clinically significant cardiovascular disease (e.g. uncontrolled hypertension, myocardial infarction, unstable angina); New York Heart Association grade II or greater congestive heart failure; serious cardiac arrhythmia requiring medication; grade II or greater peripheral vascular disease; or psychiatric illness/social situations that would limit compliance with study requirements
* Patients must not have any of the following within the 6 months prior to study drug administration: myocardial infarction, severe/unstable angina, coronary/peripheral artery bypass graft, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, or pulmonary embolism
* Patient must not have ongoing ventricular cardiac dysrhythmias of National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 4.0 grade \>= 2; patients with a history of serious ventricular arrhythmia (ventricular tachycardia \[VT\] or ventricular fibrillation \[VF\] \>= 3 beats in a row) are also excluded; additionally, patients with ongoing atrial fibrillation are not eligible
* Patients must have corrected QT (QTc) interval \< 500 msec on baseline electrocardiogram (EKG)
* Patient must not have hypertension that cannot be controlled by medications (\>= diastolic blood pressure 100 mm Hg despite optimal medical therapy)
* Patient must not have pre-existing thyroid abnormality with thyroid stimulating hormone that cannot be maintained in the normal range with medication
* If female, patient must not be pregnant or breastfeeding; all females of childbearing potential must have a blood test or urine study within 2 weeks prior to pre-registration to rule out pregnancy; if pre-registration occurs prior to surgery, the blood or urine study must be repeated within 2 weeks prior to randomization to rule out pregnancy; (note: should a woman become pregnant while participating in this study, she should inform her treating physician immediately)
* Women of child-bearing potential and men must agree to use an accepted and effective method of contraception prior to study entry and for the duration of study participation; should a woman become pregnant while participating in this study, she should inform her treating physician immediately; if a man impregnates a woman while participating in this study, he should inform his treating physician immediately as well
* Patients with known human immunodeficiency virus (HIV) are excluded
* ELIGIBILITY CRITERIA FOLLOWING RADICAL OR PARTIAL NEPHRECTOMY
* The date of randomization must be less than 12 weeks after the date of surgery; patients must have recovered from any surgical related complications
* Within 4 weeks prior to randomization, patients must meet preoperative eligibility requirements
* Patients must have histologically or cytologically confirmed renal cell carcinoma. Using 2002 (American Joint Committee on Cancer \[AJCC\] 6th edition) TNM Staging, patients must be one of the following:

  * pT1b G3-4 N0 (or pNX where clinically N0) M0
  * pT2 G (any) N0 (or pNX where clinically N0) M0
  * pT3 G (any) N0 (or pNX where clinically N0) M0
  * pT4 G (any) N0 (or pNX where clinically N0) M0 or
  * T (any) G (any) N+ (fully resected) M0

    * Patients with microvascular invasion of the renal vein of any grade or stage (as long as M0) are also eligible
    * Patients must have undergone a full surgical resection (radical nephrectomy or partial nephrectomy) by either open or laparoscopic technique; clinical evidence of lymph node positivity requires removal of all clinically positive nodes; surgeons should designate extent of node dissection; all surgical specimens must have negative margins; patients with positive renal vein margins are eligible unless there is invasion of the renal vein wall at the margin (provided no other margins are positive)
* Patients must not have collecting duct carcinomas or medullary carcinomas
* Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1
* Patients must have an absolute baseline left ventricular ejection fraction (LVEF) of \>= 50% by multigated acquisition (MUGA) scan within 4 weeks prior to randomization
* Patients must have paraffin-embedded tumor specimen available for central core review of tumor histology and other correlative studies; tumor samples will be shipped as specified
* Patients must have no evidence of residual or metastatic renal cell cancer as documented on computed tomography (CT) scans of the chest, abdomen, and pelvis, all with oral and intravenous (IV) contrast (magnetic resonance imaging \[MRI\] scans of the abdomen and pelvis with gadolinium and a non-contrast CT of the chest may be substituted if patient is not able to have CT scans with intravenous contrast); patients unable to tolerate either gadolinium or IV contrast should not participate in this study (limitations to a patient's renal function should be taken into consideration when screening for this study)
* Scans must be obtained within 4 weeks of randomization; changes on these scans that are felt to be post surgical must be documented
* Patients without reported lymph nodes in the resected surgical specimen and a reported pathologic stage (post-nephrectomy) of pNX MUST undergo a post-operative contrast-enhanced CT scan (or MRI with gadolinium) within 4 weeks of randomization to document that there is no evidence of residual disease
* Patients must not be taking cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine or phenobarbital), St John's Wort, ketoconazole, dexamethasone, the dysrhythmic drugs (terfenadine, quinidine, procainamide, sotalol, probucol, bepridil, indapamide or flecainide), haloperidol, risperidone, rifampin, grapefruit, or grapefruit juice within two weeks of randomization and during the course of therapy; (medications are not prohibited unless listed above); topical and inhaled steroids are permitted
* Patients must not receive any other investigational anti-cancer agents during the period on study
* Patients must not have a serious intercurrent illness, including ongoing or active infection requiring parental antibiotics
* Absolute granulocyte count (AGC) \>= 1,500/mm\^3
* Platelet count \>= 100,000/mm\^3
* Serum creatinine =\< 2.0 x upper limit of normal (ULN) or calculated creatinine clearance (CrCl) \>= 30 mL/min (neither drug is cleared by the kidney)
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Serum glutamic oxaloacetic transaminase (SGOT) and serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x ULN
* Patients must be able to swallow pills