Pevonedistat and Pembrolizumab for the Treatment of dMMR/MSI-H Metastatic or Locally Advanced Unresectable Solid Tumor

Inclusion Criteria: * Patients 18 years or older * Patients must have metastatic or locally advanced unresectable solid tumor * Tumor that is deficient in mismatch repair (dMMR) or microsatellite instability high (MSI-H) as determined by one of three methods: * Immunohistochemistry determined dMMR by complete loss of MLH1, PMS2, MSH2 or MSH6 * Polymerase chain reaction (PCR) determined microsatellite instability at \> 30% of tested microsatellites * Next-generation determined MSI-H based upon instability at multiple microsatellites as determined by the specific next generation sequencing panel * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Hemoglobin \>= 8 g/dL (may transfuse to achieve this threshold) * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Albumin \> 2.7 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome may enroll if direct bilirubin =\< 3 x ULN of the direct bilirubin * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3.0 x ULN * Creatinine clearance \>= 30 mL/min according to MD Anderson standard, automated laboratory calculation * Human immunodeficiency virus (HIV) patients may be considered as long as they meet the following criteria: * CD4 count \> 350 cells/mm\^3 * Undetectable viral load * No history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infec…