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 * Ab…