Testing the Effectiveness of the Anti-cancer Drug, Mirdametinib, in Treating Relapsed, Refractory Chronic Lymphocytic Leukemia

Inclusion Criteria: * Patients must have histologically or cytologically confirmed CLL or small lymphocytic lymphoma (SLL), as documented by a history at some point in time of an absolute peripheral blood B cell count \> 5000/mcL with a monoclonal B cell population coexpressing CD19, CD5, and CD23, or if CD23 negative, then documentation of the absence of t(11;14) or cyclin D1 overexpression. Alternatively, patients with lymphadenopathy in the absence of circulating disease will also be eligible for this study if lymph node biopsy or bone marrow biopsy has established the diagnosis of CLL with the above immunophenotype * Patients must have a current indication for treatment as defined by the iwCLL 2018 Guidelines (Hallek et al., 2018): * Massive or progressive splenomegaly; OR * Massive lymph nodes, nodal clusters, or progressive lymphadenopathy; OR * Grade 2 or 3 fatigue; OR * Fever ≥ 100.5°F or night sweats for greater than 2 weeks without documented infection; OR * Presence of weight loss ≥ 10% over the preceding 6 months; OR * Progressive lymphocytosis with an increase of ≥ 50% over a 2-month period or an anticipated doubling time of less than 6 months; OR * Evidence of progressive marrow failure as manifested by the development of or worsening of anemia and or thrombocytopenia * Patients must have measurable disease, defined as lymphocytosis \> 5,000/mcL, palpable or computed tomography (CT) measurable lymphadenopathy \> 1.5 cm, or bone marrow involvement \> 30% * Patients must have received at least two prior therapies for CLL including systemic therapy containing a Bruton's tyrosine kinase (BTK) inhibitor and a BCL2 inhibitor. Patients are required to have prior BTK inhibitor-based therapy because constitutive extracellular signal-regulated kinase (ERK) activation is seen in all patients with progression after BTK inhibitor therapy * Age ≥ 18 years. Because CLL is extremely rare in persons \< 18 years of age, children are excluded from this study * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%) * Absolute neutrophil count ≥ 500/mcL. Growth factor is allowed to achieve this level. Neutrophil count of 250 is permitted for patients with bone marrow involvement * Unless they have significant bone marrow involvement of CLL confirmed on biopsy * Platelets ≥ 20,000/mcL independent of transfusion within 7 days of screening. Transfusion is permitted to support platelet count for patients with bone marrow involvement * Unless they have significant bone marrow involvement of CLL confirmed on biopsy * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) unless bilirubin rise is due to Gilbert's syndrome, autoimmune hemolytic anemia,(AIHA), or of non-hepatic origin * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN * Glomerular filtration rate (GFR) 50 ml/min estimated using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) (Levey et al., 2009) * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Patients with treated brain metastases are eligible if follow-up brain imaging after central nervous system (CNS)-directed therapy shows no evidence of progression * Patients with new or progressive brain metastases (active brain metastases) or leptomeningeal disease are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class II or better * The effects of mirdametinib on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use highly effective contraception (hormonal and barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Women of child-bearing potential should also use adequate contraception for 6 months after completion of mirdametinib administration. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of mirdametinib administration. Women of childbearing age should not donate egg(s) and men should not donate sperm for the duration of study participation and 3 months after completion of mirdametinib administration Exclusion Criteria: * Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities \> grade 1) with the exception of alopecia * Patients who are receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to mirdametinib * Patients