Vaccine Therapy and Pembrolizumab in Treating Patients With Solid Tumors That Have Failed Prior Therapy

Inclusion Criteria: * Since p53 mutations occur in a wide variety of tumor types, this is a mixed histology study for incurable tumors; subjects with the following solid tumors are eligible for screening: non-small cell lung cancer, squamous cell carcinoma of the head and neck, hepatocellular carcinoma, renal cell carcinoma, melanoma, bladder, soft tissue sarcoma, triple-negative breast cancer, and colorectal carcinoma displaying microsatellite instability and pancreatic cancer * Advanced (unresectable) solid tumors: patients must have failed or been intolerant to at least one line of standard therapy or refuse standard treatment * Performance status: patients must have an Eastern Cooperative Oncology Group (ECOG) =\< 2 (Karnofsky \>= 60%) * Informed consent: all subjects must have the ability to understand and the willingness to sign an Institutional Review Board (IRB) approved consent form * Absolute neutrophil count: \>= 1,500/ul * Platelets \>= 100,000/ul * Hemoglobin level: must be greater than 9 g/dL * Renal function: calculated or measured creatinine clearance \>= 50 ml/min and/or serum creatinine =\< 1.6 mg/dl * Total bilirubin =\< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 times institutional upper normal level (AST and ALT =\< 5 times institutional upper normal level, if there is evidence of liver metastasis) * Confirmed p53 involvement: patients with p53 over-expression by immunohistochemis…