Radiation Therapy and Pembrolizumab in Treating Patients With Localized Urothelial Bladder Cancer

Inclusion Criteria: * Localized, muscle invasive urothelial carcinoma (T2-4, N0-1, M0) (mixed histology acceptable) ineligible for cystectomy * Patients must not be suitable for concurrent cisplatin as determined by the following: * Creatinine clearance less than 60ml/min; glomerular filtration rate (GFR) should be assessed by calculation from serum/plasma creatinine (Cockcroft-Gault formula) * Common Terminology Criteria for Adverse Events (CTCAE) grade (Gr) \>= 2 hearing loss * CTCAE Gr \>= 2 neuropathy * Patients must not be suitable for fluorouracil (5FU)/mitomycin chemotherapy * Subjects with not meeting the above criteria are still eligible provided the patient declines concurrent chemotherapy with radiation, after specific informed consent describing the known benefits of adding chemotherapy to the definitive bladder radiation regimen; the reason for declining must be documented * Life expectancy of at least 3 months or greater * Be willing and able to provide written informed consent/assent for the trial * Be willing to provide tissue from a newly obtained transurethral resection of bladder tumor (TURBT) or biopsy of a tumor lesion; newly-obtained is defined as a specimen obtained up to 8 weeks (56 days) prior to initiation of treatment on say 1; subjects for whom newly-obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the sponsor * Have a performance status of 0 - 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>= 1,500 /mcL, performed within 28 days of treatment initiation * Platelets \>= 100,000 / mcL, performed within 28 days of treatment initiation * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment), performed within 28 days of treatment initiation * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (GFR can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 30 mL/min for subject with creatinine levels \> 1.5 X institutional ULN, performed within 28 days of treatment initiation * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN, performed within 28 days of treatment initiation * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 X ULN, performed within 28 days of treatment initiation * Albumin \>= 2.5 mg/dL, performed within 28 days of treatment initiation * International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants, performed within 28 days of treatment initiation * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants, performed within 28 days of treatment initiation * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential must be willing to use an adequate method of contraception, for the course of the study through 120 days after the last dose of study medication * Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject * Male subjects of childbearing potential must agree to use an adequate method of contraception, starting with the first dose of study therapy through 120 days after the last dose of study therapy * Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject Exclusion Criteria: * Non-muscle invasive, localized bladder cancer (Tis, Ta, T1) * Presence of distant metastatic disease or disease not amenable to radiation treatment * Prior radiation treatment to the pelvis * Prior cystectomy * Is currently participating and receiving study therapy, or has participated in a study of an investigational agent and received study therapy, or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has a known history of active tuberculosis (TB) (Mycobacterium tuberculosis) * Hypersensitivity to pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Prior systemic chemotherapy for bladder cancer; prior intravesical chemotherapy for the treatment of non-muscle invasive urothelial bladder cancer (UBC) is allowed * Upper tract urothelial carcinoma * Has had prior chemotherapy or targeted small molecule therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known distant metastases; clinically involved pelvic nodes (N1-N3) are allowed * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; topical and inhaled corticosteroids are allowed * Has known history of, or any evidence of active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject?s participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies). * Has known active hepatitis B (e.g., hepatitis B virus surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Patients with past hepatitis B virus (HBV) infection or resolved HBV infection, defined as the presence of hepatitis B core antibody (HBc Ab) and absence of hepatitis B surface antigen (HBsAg) are eligible; HBV deoxyribonucleic acid (DNA) must be obtained in these patients prior to day 1 of therapy, but detection of HBV DNA in these patients will not exclude study participation * Patients positive for HCV antibody are eligible only if polymerase chain reaction is negative for HCV RNA * History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans) * Has a history of (non-infectious) pneumonitis that required steroids, or has current pneumonitis * Has received a live vaccine within 30 days of planned start of study therapy * Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed