Combining Azacitidine and Pembrolizumab for Hodgkin's Lymphoma

Inclusion Criteria:

* HL patients with relapse or progression. Prior checkpoint inhibitors will be allowed
* AML patients with relapse or progression. Patients may receive cytoreduction prior to enrollment for patients with rapidly proliferative disease before the start of study therapy, as needed, for clinical benefit and after discussion with the PI. Concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted
* Patients with relapsed HL involving extranodal sites
* HL patients who are not regarded as a candidate for high-dose, conventional chemotherapy
* Age of enrollment: Minimum age 1 year. No maximum age, study will include anyone in the pediatric/adolescent center
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 3 or Lansky performance status \>= 50
* Adequate renal function per age unless related to the disease
* Adequate hepatic function including total bilirubin \< 2x upper limit of normal (ULN) unless increase is due to Gilbert's disease, and AST \< 3x ULN unless considered due to lymphoma involvement.
* Provision of written informed consent or assent as per MDACC policy for study subjects.
* Females must be surgically or biologically sterile or if of childbearing potential, must have a negative serum or urine pregnancy test within 72 hours before the start of the treatment and each subsequent dose.
* Women of childbearing potential must agree to use an adequate method of contraception during the study and until 4 months after the last treatment. Males must be surgically or biologically sterile or agree to use an adequate method of contraception during the study until 1 month after the last treatment
* Males need to inform the doctor right away if the partner becomes pregnant or suspects pregnancy. While in this study and for 30 days after the last treatment the patient should not donate sperm for the purposes of reproduction. He will need to use a condom while in this study and for 30 days after the last treatment

Exclusion criteria:

* Allergy to azacitidine or pembrolizumab or the drugs' components
* Active and uncontrolled comorbidities including active uncontrolled infection, uncontrolled hypertension despite adequate medical therapy, active and uncontrolled congestive heart failure New York Heart Association (NYHA) class III/IV, clinically significant and uncontrolled arrhythmia as judged by the treating physician
* Patients with known infection with human immunodeficiency virus (HIV) or active Hepatitis B or C
* Any other medical, psychological, or social condition that may interfere with study participation or compliance, or compromise patient safety in the opinion of the investigator
* Pregnant or breastfeeding
* Has received a live vaccine within 30 days of planned start study therapy
* Current or prior use of immunosuppressive medication within 14 days prior to the first dose of pembrolizumab.

The following are exceptions to this criterion:

* Intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection)
* Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent
* Steroids as premedication for hypersensitivity reactions (eg, computed tomography \[CT\] scan premedication)
* As per Inclusion criteria #2

  * Active or prior documented autoimmune disease (including inflammatory bowel disease, celiac disease, Wegener syndrome) within the past 2 years. Subjects with childhood atopy or asthma, vitiligo, alopecia, Hashimoto syndrome, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded
  * Has known active central nervous system metastases and/or carcinomatous meningitis