Venetoclax and Romidepsin in Treating Patients With Recurrent or Refractory Mature T-Cell Lymphoma

Inclusion Criteria: * Documented informed consent of the participant and/or the legally authorized representative * Be willing to provide tissue * Eastern Cooperative Oncology Group (ECOG) =\< 2 * Resolution of all acute toxic effects of prior therapy or surgical procedures to Common Terminology Criteria for Adverse Events (CTCAE) grade =\< 1 (except alopecia) * Failed at least 2 prior systemic therapies. For anaplastic large cell lymphoma (ALCL) histologies this must include failure or intolerable side effects of brentuximab vedotin * Histologically confirmed peripheral T-cell lymphoma (PTCL) as defined by the World Health Organization (WHO) criteria 2016, excluding cutaneous T-cell lymphoma (CTCL); transformed mycosis fungoides is allowed * Measurable disease defined as: * Computed tomography (CT)/magnetic resonance imaging (MRI)/ or positron emission tomography (PET) scan, with at least one nodal site of disease which is 1.5 cm in longest dimension, and/or spleen \> 13 cm in vertical length, and/or diffuse enlargement of liver with or without focal nodules (Lugano 2014); extra nodal sites with biopsy proven abnormal lesions are allowed including skin * Patients with only bone marrow involvement will be acceptable * Prior stem cell transplant allowed * If allogeneic hematopoietic cell transplantation (HCT) must have recovered from acute toxicity * Cannot have active acute or chronic graft versus host disease (GvHD) and must be off immunosuppressive therapies * Absolute neutrophil count (ANC) \>= 1,000/mm\^3 (to be performed within 14 days prior to day 1 of protocol therapy) * NOTE: Growth factor is not permitted within 7 days of ANC assessment unless cytopenia is secondary to disease involvement * Exception: Unless documented bone marrow involvement by lymphoma * Platelets \>= 30,000/mm\^3 (to be performed within 14 days prior to day 1 of protocol therapy) * NOTE: Platelet transfusions are not permitted within 7 days of platelet assessment unless cytopenia is secondary to disease involvement * Exception: Unless documented bone marrow involvement by lymphoma * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (=\< 3 x ULN for Gilbert's syndrome or documented hepatic involvement by lymphoma) (to be performed within 14 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 3 x ULN (to be performed within 14 days prior to day 1 of protocol therapy) * If hepatic involvement by lymphoma: AST =\< 5 x ULN * Alanine aminotransferase (ALT) =\< 3 x ULN (to be performed within 14 days prior to day 1 of protocol therapy) * If hepatic involvement by lymphoma: ALT =\< 5 x ULN * Creatinine clearance of \>= 50 mL/min per 24 hour urine or the Cockcroft-Gault formula (to be performed within 14 days prior to day 1 of protocol therapy) * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by WOCBP and males of childbearing potential\* to use an adequate method of birth control (hormonal contraception is inadequate) or abstain from heterosexual activity for the course of the study through 90 days after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Bcl2 inhibitors * Any systemic anti-lymphoma therapy, including monoclonal antibody within 28 days or 5 half-lives (whichever is shorter) of initiating protocol therapy * Radiation and/or surgery (except lymph node or other diagnostic biopsies) within 14 days prior to day 1 of protocol therapy * Short course systemic corticosteroids for disease control, improvement of performance status or non-cancer indication within 7 days prior to day 1 of protocol therapy; stable ongoing corticosteroid use (i.e. at least 30 days) up to an equivalent dose of 20 mg of prednisone is permissible * Strong or moderate CYP3A inhibitors within 7 days prior to day 1 of protocol therapy * Strong or moderate CYP3A inducers within 7 days prior to day 1 of protocol therapy * P-gp inhibitors within 7 days prior to day 1 of protocol therapy * Narrow therapeutic index P-gp substrates within 7 days prior to day 1 of protocol therapy * Any other investigational agent or used an investigational device within 21 days prior to day 1 of protocol therapy * Prior surgery or gastrointestinal dysfunction that may affect drug absorption (e.g., gastric bypass surgery, gastrectomy) * Active human immunodeficiency virus (HIV) or hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who have an undetectable HIV viral load with CD4 \> 200 and are on highly active antiretroviral therapy (HAART) medication are allowed; 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; patients who have had hepatitis C but have finished treatment and are PCR negative will be allowed (testing to be done only in patients suspected of having infections or exposures) * Concurrent malignancy requiring active therapy * Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required) * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) class II to IV definitions * Patients with known cardiac abnormalities such as: * Congenital long QT syndrome * QTc (corrected QT interval on electrocardiogram \[ECG\]) interval \> 480 milliseconds * Any cardiac arrhythmia requiring anti-arrhythmic medication * Patients with a history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest, unless currently addressed with an automatic implantable cardioverter defibrillator (AICD) * Active infection requiring systemic therapy * Unable to swallow capsules, has a partial or small bowel obstruction, or has a gastrointestinal condition resulting in a malabsorptive syndrome (e.g. small bowel resection with malabsorption) * WOCBP: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)