DEC-205/NY-ESO-1 Fusion Protein CDX-1401and Decitabine in Treating Patients With Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria:

* Subjects with a confirmed diagnosis of:

  * International Prognostic Scoring System (IPSS) intermediate-I, interrnediate-2 or high-risk MDS including chronic myelomonocytic leukemia (CMML) or
  * Low blast count AML with =\< 30% blasts previously classified as refractory anemia with excess blasts in transformation who have not been previously treated with a hypomethylating agent
  * Patients with IPSS intermediate-1 disease with an isolated deletion of chromosome 5q must have previously failed treatment with lenalidomide
* Subjects with Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
* Total bilirubin =\< 2 x upper limit of normal (ULN)
* Aspartate transaminase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine transaminase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN
* Serum creatinine =\< 1.5 x ULN
* Any human leukocyte antigen (HLA) type
* Subjects of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 months after the last treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
* Subject or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure

Exclusion Criteria:

* Subjects with life-threatening illnesses other than MDS, uncontrolled medical conditions or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, or put the study outcomes at risk
* AML associated with inv(16); t(16;16); t(8;21) or t(15;17)
* Subjects with uncontrolled or symptomatic arrhythmias, or any class 3 or 4 cardiac disease as defined by the New York Heart Association functional classification
* Subjects with symptomatic central nervous system (CNS) disease which is not adequately controlled
* Subjects who have received prior radiation therapy for extramedullary disease within 2 weeks of first dose
* Subjects with human immunodeficiency virus (HIV) or active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV)
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Subjects who are being treated with systemic corticosteroids
* Subjects who have hypersensitivity to decitabine
* History of auto-immune disease (e.g. thyroiditis, lupus) except vitiligo
* Pregnant or nursing female subjects
* Unwilling or unable to follow protocol requirements
* Any condition which in the investigator's opinion deems the subject an unsuitable candidate to receive study drug
* Received an investigational agent within 30 days prior to enrollment
* Active malignancy with the exception of basal cell carcinoma, non-melanoma skin cancer, cervical carcinoma-in-situ; other prior malignancies in remission for less than 1 year
* Subjects previously treated with an allogeneic stem cell transplant