Guadecitabine and Atezolizumab in Treating Patients With Advanced Myelodysplastic Syndrome or Chronic Myelomonocytic Leukemia That Is Refractory or Relapsed

Inclusion Criteria: * Phase I: Adult subjects with advanced MDS requiring therapy who were previously treated with either azacitidine or decitabine for at least 4 cycles and deemed to have failed therapy due to progression of disease using International Working Group (IWG) criteria ("refractory") or losing their previously documented response to the therapy ("relapsed") * Phase II: Adult subjects with advanced MDS requiring therapy who were previously treated with either azacitidine or decitabine for at least 4 cycles and deemed to have failed therapy due to progression of disease using IWG criteria ("refractory") or losing their previously documented response to the therapy ("relapsed") * MDS should be classified as: * Intermediate 1-risk or higher risk according to the international prognostic scoring system (IPSS) or revised IPSS * Chronic myelomonocytic leukemia (CMML) * During the 8 weeks prior to inclusion in study, subjects must have a baseline bone marrow examination including all of the following: * Cytomorphology to confirm bone marrow blasts; * Cytogenetics; AND * Eastern Cooperative Oncology Group (ECOG) status 0-2 * Subject is able to understand and willing to comply with protocol requirements and instructions * Subject has signed and dated informed consent * Total bilirubin (except for Gilbert's syndrome) =\< 2.5 x upper limit of normal (ULN) * Aspartate aminotransferase (ALT) and alanine aminotransferase (AST) =\< 3 x ULN * Creatinine =\< 2.5 x ULN…