Azacitidine and Pembrolizumab in Treating Patients With Myelodysplastic Syndrome

Inclusion Criteria: * Voluntary signed informed consent before performance of any study related procedure not part of normal medical care indicating that the patient is aware of the investigation and nature of this study in keeping with institutional policies and with the understanding that the consent may be withdrawn with the subject at any time without prejudice to future medical care * Intermediate 1 (INT-1) or higher risk MDS defined by International Prognostic Scoring System (IPSS) criteria * Patients can or cannot have receive prior therapy with hypomethylating agent but will be allocated to specific patient cohorts based on their prior exposure. Patients that had received prior hypomethylating agent therapy should have at least received 6 cycles of therapy and not achieved any response or had progressed after any given number of cycles * Eastern Cooperative Oncology Group (ECOG) performance of 0 to 2 * Male patients, even if surgically sterilized, should agree to practice effective barrier contraception for the entire study treatment period and through 120 days after the last dose of the study treatment or agree to completely abstain from heterosexual intercourse. Female patients who are postmenopausal for at least one year before the screening visit or are surgical sterile or if they are of child bearing potential must have a negative pregnancy test within 72 hours of treatment of the start date and agree to practice two effective methods of contraception forms at the same time from the time of signing the informed consent through 120 days of the last dose of the study treatment or agree to completely abstain from heterosexual intercourse * Willingness and ability to comply with scheduled visits treatment plans, laboratory tests and other study procedures * Serum creatinine or measured or calculated creatine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrcL\]) =\< 2.0 x upper limit of normal (ULN) or \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (performed within 10 days of treatment initiation). Creatinine clearance should be calculated per institutional standard * Serum total bilirubin =\< 2.0 x ULN (unless considered due to Gilbert's disease or leukemia disease) or direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (performed within 10 days of treatment initiation) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x ULN (unless considered due to Gilbert's disease or leukemia disease) or =\< 5 x ULN for subjects with liver metastases (performed within 10 days of treatment initiation) * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy * Patients must receive a minimum dose of azacitidine of 75mg/(m)(2) dose Exclusion Criteria: * Significant medical psychiatric cognitive or other conditions that may compromise the patient ability to understand the patient information to give informed consent to comply with the study protocol or to complete the study * Any severe or concurrent disease or condition including uncontrolled systemic infection, congestive heart failure, angina pectoris or cardiac arrhythmia and autoimmune processes that in the opinion of the investigator would make the patient inappropriate for study participation * Patients with known hypersensitivity to 5-azacitidine or MK3475 or any of their excipients * Prior history of stem cell transplantation * For patients in the relapse or refractory cohort, any other therapy not being a hypomethylating agent after hypomethylating agents (HMA) failure or more than 4 months since completion of last cycle of hypomethylating agent. Please note that hypomethylating agent may include second generation compounds such as SGI-110, oral decitabine or oral azacitidine and will also include combinations with investigational agents * Treatment with other investigational agents including chemotherapy, immunotherapy, or radiation therapy within a month prior to the start of this clinical trial * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has a known history of active TB (Bacillus tuberculosis) * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent. Note: Subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study. Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has known history of, or any evidence of active, non-infectious pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days of planned start of study therapy. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed