Nivolumab After Combined Modality Therapy in Treating Patients With High Risk Stage II-IIIB Anal Cancer

Inclusion Criteria: * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Age \>= 18 years * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Patients must have histologically proven stage IIB (T3N0M0 only), IIIA (T2N1M0), IIIB (T4N0M0), or IIIC (T3N1M0, T4N1M0) invasive squamous cell carcinoma of the anus or anorectum, according to the American Joint Committee on Cancer (AJCC) 8th edition; this may include tumors of non-keratinizing histology such as basaloid, transitional cell, or cloacogenic histology; individuals with squamous cell carcinoma of the anal margin are eligible if there is evidence of extension of the primary tumor into the anal canal * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Patients must have hemoglobin levels of \> 9 g/dL (within 2 weeks prior to registration) * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Patient must have a platelet count of \> 100,000/mm\^3 (within 2 weeks prior to registration) * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Patient's absolute neutrophil count (ANC) level must be \> 1500/mm\^3 (within 2 weeks prior to registration) * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Serum creatinine must be =\< 1.5 X upper limit of normal (ULN) (within 2 weeks prior to registration) * REGISTRATION TO STEP 1 ELIGIBILITY CRITERIA: Total bilirubin must be \< 2 X ULN (within 2 weeks prior to registration) * REGISTRATION…