Ibrutinib and Azacitidine for Treatment of Higher Risk Myelodysplastic Syndrome

Inclusion Criteria: * Pathologically confirmed diagnosis of myelodysplastic syndrome * Revised international prognostic scoring system (IPSS-R) intermediate, high or very high * For the dose escalation cohorts, any prior number of MDS therapies, including hypomethylating agents, are permitted; for the dose expansion cohort, subjects must be azacitidine naïve, but otherwise any prior number of MDS therapies are permitted; treatment naïve patients are eligible for both the dose escalation and expansion cohorts if they are unfit for or refuse intense therapy * No specific hematologic parameters for study entry are required; transfusion-dependent patients are eligible and platelet counts should be maintained greater than 10,000/mm\^3 * Serum aspartate transaminase (AST) and alanine transaminase (ALT) =\< 3.0 x upper limit of normal (ULN) * Estimated creatinine clearance \>= 30 ml/min (Cockcroft-Gault) * Bilirubin =\< 1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 x ULN and partial thromboplastin time (PTT) (activated \[a\]PTT) \< 1.5 x ULN * Karnofsky performance status (KPS) performance status of 60% or greater * Female subjects who are of non-reproductive potential (ie, post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy); or, female subjects of childbearing potential must have a negative serum pregnancy test upon study entry * Male and female subjects who agree to use highly effective methods of birth control during the period of therapy and for 30 days after the last dose of study drug Exclusion Criteria: * Known bleeding disorders, active bleeding disorders or clinical signs of bleeding (grade \>= 2) * Prior bone marrow transplant within 3 months or with acute graft versus host disease (GVHD) * Prior treatment with a Bruton's tyrosine kinase (BTK) inhibitor * Anticancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal or any investigational therapy within 14 days or 5 half-lives prior to first dose of study drug * Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version 4.03), grade =\< 1, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia * History of other malignancies, except: * Malignancy treated with curative intent and with no known active disease present for \>= 1 years before the first dose of study drug and felt to be at low risk for recurrence by treating physician * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease * Low-risk prostate cancer after curative surgery * Concurrent systemic immunosuppressant therapy * Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Recent infection requiring intravenous systemic treatment * History of stroke or intracranial hemorrhage within 6 months prior to enrollment * Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded * Major surgery within 4 weeks of first dose of study drug * Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to enrollment * Unable to swallow capsules or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction * Concomitant use of warfarin or other vitamin K antagonists * Requires treatment with a strong cytochrome P450 (CYP) family 3, subfamily A, polypeptide 4/5 (3A4/5) inhibitor * Lactating or pregnant * Unwilling or unable to participate in all required study evaluations and procedures * Unable to understand informed consent form (ICF)