Ipilimumab and/or Nivolumab in Combination With Temozolomide in Treating Patients With Newly Diagnosed Glioblastoma or Gliosarcoma

Inclusion Criteria: * Histopathologically proven diagnosis of glioblastoma or gliosarcoma prior to registration by pathology report * The tumor must be unifocal, confined to the supratentorial compartment and have undergone a gross total or near gross total resection; this will increase the likelihood that the patient will not require corticosteroids or develop pseudoprogression * The formalin-fixed, paraffin-embedded (FFPE) tumor tissue block must be available to be sent for retrospective central pathology review after registration * Patients must be registered within 35 days of completion of chemoradiation * History/physical examination within 7 days prior to registration * Patients must have undergone an evaluation by magnetic resonance imaging (MRI) within 35 days of completing radiation and must also be within 7 days prior to registration; MRI must NOT demonstrate tumor progression, but patients with imaging changes consistent with pseudo-progression, stable neurologic function and not needing corticosteroid treatment are eligible * Karnofsky performance status \>= 70 within 7 days prior to registration * Absolute neutrophil count \>= 1,500 cells/mm\^3 * Platelet count \>= 100,000 cells/mm\^3 * Hemoglobin (Hgb) \> 9 g/dL (can be achieved with transfusion) * Blood urea nitrogen (BUN) =\< 30 mg/dl * Serum creatinine =\< 1.7 mg/dl * Total bilirubin (except patients with Gilbert's syndrome, who are eligible for the study but exempt from the total bilirubin eligibility criterion) =\< 2.0 mg/dl * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x upper limit of normal (ULN) * The patient must have completed chemoradiation (all cohorts) within standards of care established by prior Radiation Therapy Oncology Group (RTOG)/Network Radiotherapy Group (NRG) Oncology studies as follows: * Radiation therapy * Modality: either 3-dimensional (3D) or intensity-modulated radiation therapy (IMRT), or proton therapy is allowed * Time to initiation: radiotherapy must be initiated within or equal to 42 days after surgery * Target volumes: target volume definition will be based upon postoperative-enhanced MRI; preoperative imaging should be used for correlation and improved identification, as necessary * Dose guidelines: the initial target volume will be treated to 46 Gray (Gy) in 23 fractions; after 46 Gy, the cone-down or boost volume will be treated to a total of 60 Gy, with seven additional fractions of 2 Gy each (14 Gy boost dose) * Temozolomide during concomitant radiation therapy * Temozolomide must have been administered continuously from day 1 of radiotherapy to the last day of radiation (+/- 3 days to take into consideration holidays) at a daily oral dose of 75 mg/m\^2 for a maximum of 49 days (except missed doses due to toxicity) * The patient must not be on a corticosteroid dose greater than physiologic replacement dosing defined as 30 mg of cortisone per day or its equivalent * The patient must provide study-specific informed consent prior to study entry * Echocardiogram (ECHO) cardiogram and cardiology consultation required within 7 days prior to registration for patients with a history of congestive heart failure or cardiovascular disease or history of exposure to cardiotoxic agents who are not already excluded Exclusion Criteria: * Definitive clinical or radiologic evidence of progressive disease * Prior placement of Gliadel wafer or local brachytherapy * Use of an immunotherapy such as a vaccine therapy, dendritic cell vaccine or intracavitary or convectional enhanced delivery of therapy * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years * Unstable angina within the last 6 months prior to registration * Transmural myocardial infarction within the last 6 months prior to registration * Evidence of recent myocardial infarction or ischemia by the findings of S-T elevations of \>= 2 mm using the analysis of an electrocardiogram (EKG) performed within 7 days prior to registration * New York Heart Association grade II or greater congestive heart failure requiring hospitalization within 12 months prior to registration * History of stroke, cerebral vascular accident (CVA) or transient ischemic attack within 6 months prior to registration * Serious and inadequately controlled cardiac arrhythmia * Significant vascular disease (e.g., aortic aneurysm, history of aortic dissection) or clinically significant peripheral vascular disease * Evidence of bleeding diathesis or coagulopathy * Serious or non-healing wound, ulcer, or bone fracture or history of abdominal fistula, gastrointestinal perforation, intra-abdominal abscess major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to registration, with the exception of the craniotomy for tumor resection * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration * Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; note, however, that laboratory tests for additional liver function tests and coagulation parameters are not required for entry into this protocol * Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note, however, that human immunodeficiency virus (HIV) testing is not required for entry into this protocol * Active connective tissue disorders, such as lupus or scleroderma, which in the opinion of the treating physician may put the patient at high risk for immunologic toxicity * Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded; these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome or chronic inflammatory demyelinating polyneuropathy (CIDP), myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IBD), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded * Of note, patients with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible; patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible * Any other major medical illnesses or psychiatric impairments that in the investigator's opinion will prevent administration or completion of protocol therapy * Pregnancy or lactating females; women of childbearing potential must have a negative serum pregnancy test within 7 days prior to registration * History of severe hypersensitivity reaction to any monoclonal antibody