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

Inclusion Criteria: * Understand and voluntarily sign an informed consent form * Age \>/=18 years at the time of signing the informed consent form * Diagnosis of AML \[other than acute promyelocytic leukemia (APL)\] with refractory/relapsed disease; patients with relapsed/refractory high-risk \[(intermediate-2 or higher by International Prognostic Scoring System (IPSS) and/or \>/= 10% blasts)\] MDS will also be eligible. (Treatment approach for relapsed/refractory AML is very similar to that of high risk MDS), or diagnosis of relapsed/refractory T-ALL/T-LBL. * All non-hematological toxicity of previous cancer therapy should have resolved to =\< grade 1 (except alopecia or other toxicities not involving major organs) * Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 at study entry * Serum creatinine \</= 2 mg/dL and estimated glomerular filtration rate or creatinine clearance \>/= 40 ml/min * Total bilirubin =\< 2 mg/dL * Aspartate aminotransferase (AST) and/or alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN) * Women of childbearing potential must be practicing a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies: eg, established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device or intrauterine system; barrier methods: condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization (the vasectomized partner should be the sole partner for that subject); true abstinence (when this is in line with the preferred and usual lifestyle of the subject) during and after the study (3 months after the last dose of daratumumab for women) * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control eg, either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm during the study and for 3 months after receiving the last dose of study drug * AML relapse \> 6 months since autologous or allogeneic stem cell transplantation, provided there is no active graft-versus-host disease (GVHD) \> grade 1; no treatment with high dose steroids for GVHD (up to 20 mg prednisolone or equivalent); no treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus (blood levels of 0.5-0.6 ug/mL) Exclusion Criteria: * White blood cell count more than 25 × 109 /L prior to initiation of venetoclax * Pregnant or breast feeding females * Cancer chemotherapy within 2 weeks prior to start of daratumumab treatment (exception hydroxyurea). Use of hydroxyurea to control proliferative disease will be allowed prior to starting therapy on study and for 7 days during cycle 1-3 (maximum daily dose of 7 gm) * Subject has received daratumumab or other anti-CD38 therapies previously * Subject has received a cumulative dose of corticosteroids more than the equivalent of \>= 140 mg of prednisone within the 2 week period before cycle 1, day 1 * Subject has known chronic obstructive pulmonary disease (COPD) with a forced expiratory volume in 1 second (FEV1) \< 50% of predicted normal. NOTE: FEV1 testing is required for patients suspected of having COPD and subjects must be excluded if FEV1 \< 50% of predicted normal * Subject has a history of another malignancy within 5 years before cycle 1, day 1 (exceptions are squamous and basal cell carcinomas of the skin and carcinoma in situ of the cervix, or malignancy that in the opinion of the investigator, with concurrence with the IND office and supporter's medical monitor, is considered cured with minimal risk of recurrence) * Subject is known to be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen \[HBsAg\]). Subjects with resolved infection (ie, subjects who are HBsAg negative but positive for antibodies to hepatitis B core antigen \[anti-HBc\] and/or antibodies to hepatitis B surface antigen \[anti- HBs\]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels. Those who are PCR positive will be excluded. EXCEPTION: Subjects with serologic findings suggestive of HBV vaccination (anti-HBs positivity as the only serologic marker) AND a known history of prior HBV vaccination, do not need to be tested for HBV DNA by PCR * Subjects who are seropositive for hepatitis C (except in the setting of a sustained virologic response \[SVR\], defined as aviremia at least 12 weeks after completion of antiviral therapy) will be excluded. * Subject has clinically significant cardiac disease, including: myocardial infarction within 1 year before Cycle 1, Day 1, or unstable or uncontrolled disease/condition related to or affecting cardiac function (e.g., unstable angina, congestive heart failure, New York Heart Association Class III-IV); cardiac arrhythmia (Common Terminology Criteria for Adverse Events \[CTCAE\] version 4.03 grade 2 or higher) or clinically significant electrocardiogram (ECG) abnormalities; screening 12-lead ECG showing a baseline QT interval as corrected by Fridericia's formula (QTcF) \> 470 msec * Subject has known severe allergies, hypersensitivity, or intolerance to monoclonal antibodies or human proteins, or their excipients (refer to the latest version of the Investigator Brochure), or known sensitivity to mammalian-derived products * Subject has any concurrent medical condition or disease (eg, active systemic infection, laboratory abnormalities) that is likely to interfere with study procedures or results, or that in the opinion of the investigator would constitute a hazard for participating in this study * Exclude patients with known Kell antibodies