Pembrolizumab After Radiation Therapy in Treating Patients With Pleural Malignant Mesothelioma

Inclusion Criteria: * Patients must have a histologic diagnosis of malignant pleural mesothelioma, with histologic diagnosis from the pleura or relevant lymph node stations, including mediastinal, hilar, or supraclavicular lymph nodes * Be willing and able to provide written informed consent/assent for the trial * Have measurable or non-measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1; however, note that patients in Cohort 1 that have undergone an R0 resection will be eligible for the trial * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale * Absolute neutrophil count (ANC) \>=1,500 /mcL (within 10-15 days of treatment initiation) * Platelets \>= 100,000 /mcL (within 10-15 days of treatment initiation) * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment) (within 10-15 days of treatment initiation) * Serum creatinine =\< 1.5 X upper limit of normal (ULN) or measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN (within 10-15 days of treatment initiation) * Serum total bilirubin =\< 1.5 X ULN or direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (within 10-15 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 or =\< 5 X ULN for subjects with liver metastases (within 10-15 days of treatment initiation) * Albumin \>= 2.5 mg/dL (within 10-15 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 (within 10-15 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 (within 10-15 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 should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should 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 * COHORT 1 (PATIENTS RECEIVING HEMITHORACIC RADIATION THERAPY) * Patients must not have evidence of metastatic disease per positron emission tomography (PET)/ computed tomography (CT) scan; mediastinal lymph node involvement is acceptable * Patients will have received at least 2 cycles of induction chemotherapy with pemetrexed/cisplatin or pemetrexed/carboplatin * Forced expiratory volume in 1 second (FEV1) \>= 30% of predicted postoperative (ppoFEV1, as if patient underwent a pneumonectomy) * Diffusing capacity of the lungs for carbon monoxide (DLCO) \> 35% predicted * Patients must be assessed to be a suitable candidate for hemithoracic radiation therapy per the treating radiation oncologist; if the patient undergoes pleurectomy/decortication, they must initiate hemithoracic radiation therapy within 4 months of the surgery date; patients that do not meet the dose constraints outlined below will be removed from the study prior to radiation therapy * COHORT 2 INCLUSION CRITERIA * Patients must be assessed to be a suitable candidate for radiation therapy by the treating radiation oncologist; patients that do not meet the dose constraints outlined below will be removed from the study prior to radiation therapy * Any prior number of prior therapies, including prior immunotherapy, is allowed * Patient must have prior treatment with a platinum plus pemetrexed regimen Exclusion Criteria: * 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; note that patients should not receive steroids during pembrolizumab administration * Has a known history of active tuberculosis (TB) (Bacillus 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 * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 and who have not recovered adequately from this treatment (=\< grade 2 toxicity at the time of enrollment) * Has a known additional malignancy that is progressing or requires active treatment; patients with a stage I-III cancer that has been cured over two years ago are not excluded in the study * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * 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 (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis * Has an active infection requiring systemic therapy * 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 a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * 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 * Evidence of interstitial lung disease * COHORT 1 EXCLUSION CRITERIA * Patients undergoing an extrapleural pneumonectomy (EPP); lung sparing surgeries, such as pleurectomy/decortication, are acceptable * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent * COHORT 2 EXCLUSION CRITERIA * Patients in which hemithoracic radiation therapy is planned * Patients who have received EPP for mesothelioma * COHORTS 1 AND 2 EXCLUSION CRITERIA * Patients with inherited syndromes associated with hypersensitivity to ionizing radiation, specifically patients with known history of ataxia-telengiectasia, Nijmegen breakage syndrome