Ipilimumab and Decitabine in Treating Patients With Relapsed or Refractory Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria: * Subjects with evidence of AML or myelodysplastic syndrome (MDS) that meet at least one of the following criteria: * Relapsed AML: evidence of \>= 5% blasts in the bone marrow; or reappearance of blasts in the peripheral blood; or development of extramedullary disease (according to 2003 IWG criteria) who relapse after: * Allogeneic hematopoietic stem cell transplant, or * After one cycle of standard cytotoxic chemotherapy or two cycles of any hypomethylating agent-based therapy * Refractory AML: =\< 2 prior induction regimens (example: patients who receive 7+3 followed by 5+2 would count as one induction regimen) or a minimum of two cycles of any hypomethylating agent-based therapy * Treatment-naive AML: must be 75 years and older with de novo or secondary AML to be considered eligible * Relapsed MDS: disease recurrence after CR, partial remission (PR) or hematologic improvement with bone marrow blasts \>= 5% who relapse after: * Allogeneic hematopoietic stem cell transplant, or * After four cycles of any hypomethylating agent-based therapy * Refractory MDS: disease progression at any time after initiation of hypomethylating agent treatment or persistent bone marrow blasts \>= 5% despite a minimum of four cycles of hypomethylating agent therapy * Untreated or previously treated therapy- related or secondary MDS * Allowed prior allogeneic hematopoietic stem cell transplantation (allo-HCT) regardless of stem cell source; patients must be at least 3 months post allo-HCT (at time of treatment start); mismatched transplantations would be allowed * Patients must be off systemic immunosuppressive medications \> 2 weeks prior to treatment start; if patients are in systemic corticosteroids and must be on a dose of prednisone 5 mg/day or less (or equivalent), then patients must be on this reduced dose for \> 1 week prior to treatment start; topical steroids are allowed * If post allo-HCT, then patient must have baseline donor T cell chimerism of \>= 20% (from peripheral blood); evaluation can be made within 4 weeks of treatment start * No limitations on prior therapies * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 1.5 x local institutional upper limit of normal (ULN) * If elevated total bilirubin is due Gilbert's disease or disease-related hemolysis then total bilirubin =\< 3.0 x local institutional ULN * Aspartate aminotransferase (AST) or serum glutamic oxaloacetic transaminase (SGOT) =\< 3.0 x local institutional ULN * Alanine aminotransferase (ALT) or serum glutamic pyruvic transaminase (SGPT) =\< 3.0 x local institutional ULN * Serum creatinine =\< 2.0 x local institutional ULN * Negative serum pregnancy test for women who are of child bearing potential (test must be repeated if performed \> 72 hours from treatment start); the effects of ipilimumab on the developing human fetus are unknown; for this reason and because immunotherapy agents as well as decitabine are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after study drug administration * Patients with known active human immunodeficiency virus (HIV) infection; patients with chronic HIV with a CD4 \> 250, undetectable viral load by polymerase chain reaction (PCR), without opportunistic infection, and on a stable regimen of highly active anti-retroviral therapy (HAART) therapy would be eligible * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 2 weeks prior to treatment start or those who have not recovered from adverse events due to agents administered more than 2 weeks prior to treatment start * Hydroxyurea is allowed for symptomatic leukocytosis if clinically necessary; a total white blood cell (WBC) count \< 25 x 10\^9/L prior to first dose of decitabine on trial is required; prior leukapheresis and/or prior or concurrent treatment with hydroxyurea to achieve this level are allowed * Ongoing concurrent hormonal therapy is allowed * Participants with known central nervous system (CNS) involvement with leukemia or who are receiving intrathecal chemotherapy for active CNS leukemia * Those with a history of CNS involvement that has been completely treated and those who require intrathecal chemotherapy prophylaxis are eligible in the expansion cohorts * Prior hypomethylating agent (HMA) therapy is allowed, however this study excludes patients with progression or relapse that occur while receiving HMA-based therapy within 12 weeks prior to treatment start on study; disease progression is defined as either: (1) patients with prior MDS who progress to AML (defined by the presence of \>= 20% blasts in peripheral blood or bone marrow) on HMA-based therapy; OR (2) patients with AML with evidence of progressive disease according to European Leukemia Net \[ELN\] 2017 criteria) (e.g. \> 50% increase in marrow blasts over baseline or \> 50% increase in peripheral blasts to \> 25 x 10\^9/L (\> 25,000/uL) (in absence of differentiation syndrome) * (Note: Patients who relapse post-transplant who received HMA treatment prior to transplant are eligible for study) * Donor lymphocyte infusion within 8 weeks prior to treatment start if post-transplant * For patients that are post-transplant, ineligible patients include those with a history of overall grade III or IV (severe) acute GVHD at any time even if resolved * Patients with a history of prior treatment with anti-CTLA-4, anti-PD 1 antibody, or anti-PDL1 antibody * Participants who are receiving any other investigational agents * Participants with known CNS involvement with leukemia or who are receiving intrathecal chemotherapy that is either prophylactic or therapeutic; history of CNS involvement that has been completely treated (no longer receiving intrathecal chemotherapy) will be allowed * 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; any other prior or ongoing condition, in the opinion of the investigator, that could adversely affect the safety of the patient or impair the assessment of study results; as patients with AML and MDS are prone to infections, if patients are actively being treated with appropriate antibiotics or antifungal therapy with clinical evidence of infection control, then they will be considered eligible for study * Autoimmune disease: Patients who are not eligible include those 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 a history of autoimmune disease (specifically including: diabetes mellitus, vitiligo, Hashimoto's thyroiditis) who are asymptomatic, do not require immune suppression or steroids, and do not have threatened vital organ function from these conditions may be considered after discussion with the principal investigator (PI) * No concurrent active malignancies are allowed on study for \>= 2 years prior to treatment start with the exception of currently treated basal cell or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or breast * Patients with known active hepatitis B virus (HBV) infection should be excluded because of potential effects on immune function and/or drug interactions; however, if a patient has HBV history with an undetectable HBV load by polymerase chain reaction (PCR), no liver-related complications, and is on definitive HBV therapy, then he/she would be eligible for study * Patients with known active hepatitis C virus (HCV) infection; patients with a history of HCV infection who received definitive therapy and has an undetectable viral load by PCR would be eligible * Pregnant women are excluded from this study because ipilimumab has the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with ipilimumab, breastfeeding should be discontinued if the mother is treated with ipilimumab; these potential risks may also apply to decitabine