Ipilimumab in Treating Patients With Relapsed or Refractory High-Risk Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria: * Patients must be able to understand and voluntarily sign an informed consent form * Able to adhere to the study visit schedule and other protocol requirements * Life expectancy of greater than 6 months * Must have one of the following diagnoses: * Pathologically confirmed chronic myelomonocytic leukemia (CMML) or myelodysplastic syndromes (MDS) with high risk features at the time of referral for trial as defined by: * Intermediate (INT)-2 or high International Prognostic Scoring System (IPSS) score * Secondary MDS (defined as MDS developing in a patient with an antecedent hematologic disorder or any patient with prior chemotherapy or radiation exposure) * INT-1 MDS with excess blasts (\>= 5% blasts in bone marrow \[BM\]) or red blood cell (RBC) transfusion-dependency * MDS progressing to oligoblastic acute myeloid leukemia (AML) with 21-30% BM blasts * CMML with \>= 5% marrow blasts, or RBC or platelet transfusion-dependency, abnormal karyotype, or proliferative features (white blood cell count \>=13,000/uL, splenomegaly on physical examination, or extramedullary disease) * All patients are required to have failed to respond or relapsed after an initial response to hypomethylating agents 5-azacitidine or decitabine or have refused to receive hypomethylating therapy; failure to respond is defined as failing to achieve a CR, PR or HI after at least 4 cycles of hypomethylating therapy; these patients could have received other therapies or not, but must have received hypomethylating therapy or have refused to receive hypomethylating therapy * Pathologically confirmed AML patients who have received one or two courses of induction chemotherapy or hypomethylating agent therapy AND no plans for further chemotherapy therapy, but remain with residual disease of \< 5% blasts in BM, by morphology, cytogenetics, fluorescent in situ hybridization (FISH), polymerase chain reaction (PCR) or flow cytometry * Patients must not have received any other treatment for their disease, including hematopoietic growth factors, within three weeks of beginning the trial, and should have recovered from all toxicities of prior therapy (to grade 0 or 1) * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 at study entry ECOG, or Karnofsky \>= 60% * Calculated creatinine clearance by Modification of Diet in Renal Disease (MDRD) (CrCL) \> 50 ml/min/1.73 squared meter * Total bilirubin =\< 2.0 mg/dL unless due to Gilbert's syndrome, hemolysis, or ineffective hematopoiesis * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x upper limit of normal (ULN) * Females of childbearing potential must have a negative serum or urine pregnancy test within 72 hours prior to start of ipilimumab * Patients must have no clinical evidence of central nervous system (CNS) or pulmonary leukostasis, disseminated intravascular coagulation, or CNS leukemia * Patients must have no serious or uncontrolled medical conditions Exclusion Criteria: * Any serious medical condition, uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, laboratory abnormality, or psychiatric illness/social situations that would limit compliance with study requirements or prevent the subject from signing the informed consent form * Pregnant or breast feeding females (lactating females must agree not to breast feed while taking ipilimumab) * Any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Use of any other experimental drug or therapy within 21 days of baseline * Known hypersensitivity to ipilimumab or history of allergic reactions attributed to compounds of similar chemical or biologic composition to ipilimumab * Prior use of ipilimumab, other cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) blocking therapies, anti-programmed cell death 1 (PD 1) antibody, cluster of differentiation (CD) 137 agonist or other immune activating therapy such as anti-CD 40 antibody within the last 3 months of enrollment in the study; if any of these of these agents were used more than 3 months earlier to enrollment in study, the patient should have recovered from all toxicity and at least 3 months had passed since last use to allow for clearance and observation of any other side effects from the previous therapy * Concurrent use of other anti-cancer agents or treatments, including other investigational agents * Autoimmune disease: patients with a history of inflammatory bowel disease, including ulcerative colitis and Crohn's disease, are excluded from this study, as are patients with a history of symptomatic disease (e.g., rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's granulomatosis\]); CNS or motor neuropathy considered of autoimmune origin (e.g. Guillain-Barre syndrome and Myasthenia Gravis, multiple sclerosis) * Patients with known immune impairment who may be unable to respond to anti-CTLA-4 antibody * Patients with known evidence of active cancers, or other cancer under active treatment; exceptions include patients with no evidence of disease receiving adjuvant hormone-based therapy or either breast or prostate cancer * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients with chronic human immunodeficiency virus (HIV), hepatitis B or hepatitis C infections should be excluded because of potential effects on immune function and/ or possible drug interactions * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with ipilimumab