Bevacizumab, Radiation Therapy, and Combination Chemotherapy in Treating Patients Who Are Undergoing Surgery for Locally Advanced Nonmetastatic Rectal Cancer

Inclusion Criteria: * Patients must have histologically confirmed, locally advanced, non-metastatic primary T3 or T4 adenocarcinoma of the rectum * Patients must not have evidence of tumor outside of the pelvis including liver metastases, peritoneal seeding, or metastatic inguinal lymphadenopathy * Patients must not have intra-operative radiotherapy (IORT) or brachytherapy treatment to the pelvis * The distal border of the tumor must be at or below the peritoneal reflection, defined as within 12 centimeters of the anal verge by proctoscopic examination * Transmural penetration of tumor through the muscularis propria must be demonstrated by either of the following: computed tomography (CT) scan plus endorectal ultrasound, or a magnetic resonance imaging (MRI); an endorectal coil or pelvic MRI is allowed * For the patient to be eligible, the surgeon must prospectively define the tumor as either initially resectable or potentially resectable after pre-operative chemoradiation; clinically resectable tumors are defined as completely resectable with negative margins based on routine examination of the non-anesthetized patient; patients whose tumors are not resectable are not eligible; before pre-operative (op) treatment, the surgeon should estimate and record the type of resection anticipated: pelvic exenteration, posterior pelvic exenteration, APR, LAR, or LAR/coloanal anastomosis * Patients with tumors that are clinically fixed, clinical stage T4N0-2, M0 are eligible if it is believed that their tumors are potentially resectable after chemoradiation; based on the following: * Clinically fixed tumors on rectal examination with tumor adherent to the pelvic sidewall or sacrum * Sciatica attributed to sacral root invasion with CT scan/MRI evidence of the lack of clear tissue plane will be considered evidence of fixation * Hydronephrosis on CT scan or intravenous pyelogram (IVP) or ureteric or bladder invasion as documented by cystoscopy and cytology or biopsy, or invasion into prostate * Vaginal or uterine involvement * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * A surgical evaluation must confirm patient's ability to tolerate the proposed surgical procedure * Patients must have a caloric intake \> 1500 kilocalories/day (d) * Within 4 weeks prior to registration, the patient's absolute neutrophil count (ANC) level must be \>= 1,500/mm\^3 * Within 4 weeks prior to registration, the patients platelet level must be \>= 100,000/mm\^3 * Within 4 weeks prior to registration, serum creatinine must be \< 1.5 X upper limit of normal (ULN); if serum creatinine \> 1.5 x ULN, then creatinine clearance must be \>= 50 mL/mm * Within 4 weeks prior to registration, serum bilirubin must be =\< 1.5 X ULN * Within 4 weeks prior to registration, alkaline phosphatase (alk phos) must be \< 2 x ULN * Within 4 weeks prior to registration, serum glutamic oxaloacetic transaminase (SGOT) must be \< 2 x ULN * Carcinoembryonic antigen (CEA) must be determined prior to initiation of therapy * Within 4 weeks prior to registration, urine protein/creatinine (UPC) ratio must be \< 1; patients with a ratio of \>= 1 must undergo a 24-hour urine collection which must be an adequate collection and must demonstrate \< 1 gram (gm) of protein in order to participate * Within 4 weeks prior to registration, albumin must be \>= 2 gm/dl * Absence of clinical evidence of high-grade (lumen diameter \< 1 cm) large bowel obstruction, unless diverting colostomy has been performed * Eligible patients of reproductive potential (both sexes) must agree to use an accepted and effective method of contraceptive during study therapy and for at least 6 months after the completion of bevacizumab * Women must not be pregnant or breast-feeding; all females of childbearing potential must have a serum pregnancy test to rule out pregnancy within 2 weeks of registration * Patients must have had no prior chemotherapy for rectal cancer or pelvic irradiation therapy * Patients with prior malignancies, including pelvic cancer, are eligible if they have been disease free for \> 5 years; patients with prior in situ carcinomas are eligible provided there was complete removal * Patients must have no active inflammatory bowel disease or other serious medical illness or disease that might limit the patient's ability to receive protocol therapy * Patients with a history of cerebrovascular accident (CVA)/transient ischemic attack (TIA) at any time, or myocardial infarction/unstable angina within 12 months of study entry are not eligible * Patients with \> grade 1 peripheral neuropathy are not eligible * Patients must have urine protein/creatinine (UPC) ratio of \< 1.0; patients with a UPC ratio \>= 1.0 must undergo a 24-hour urine collection, which must be an adequate collection and must demonstrate \< 1 gm of protein in order to participate * Patients with a history of hypertension must measure \< 150/90 mmHg and be on a stable regimen of anti-hypertensive therapy * Patients with clinically significant peripheral vascular disease are not eligible * Patients must not have any of the following: * Unstable angina (within 12 months of study entry) * New York Heart Association (NYHA) grade II or higher congestive heart failure * Evidence of bleeding diathesis/coagulopathy * Serious non-healing wound or bone fracture * Patients with a history of the following within 28 days prior to registration are not eligible: * Abdominal fistula * Gastrointestinal perforation * Intrabdominal abscess * Patients with a history of the following within 28 days prior to day 0 (first treatment day) are not eligible: * Major surgical procedure * Open biopsy * Significant traumatic injury * Patients must not have core biopsy within 7 days prior to day 0 (first treatment day) * Patients with prothrombin time (PT) (international normalized ratio \[INR\]) \> 1.5 are not eligible, unless the patient is on full-dose anticoagulants; if so, the following criteria must be met for enrollment: * The subject must have an in-range INR (usually between 2 and 3), be on a stable dose of warfarin or on a stable dose of low molecular weight heparin * The subject must not have active bleeding or a pathological condition that is associated with a high risk of bleeding