A Phase 1 Study of Combination Tovorafenib (DAY101) and Rituximab Treatment in Relapsed or Refractory Classical Hairy Cell Leukemia and Phase 2 Randomized Study Comparing Tovorafenib (DAY101) and Rituximab With Cladribine and Rituximab for Front-Line Treatment of Classical Hairy Cell Leukemia

Inclusion Criteria: * Patients must have histologically or cytologically confirmed diagnosis of classical hairy cell leukemia (HCL), including demonstration of BRAF V600E mutation by immunohistochemistry, molecular diagnostic testing, or polymerase chain reaction (PCR) * PHASE 1 ONLY: Prior therapy with at least one purine nucleoside analog-containing regimen (fludarabine, pentostatin, or cladribine) unless contraindicated. Prior vemurafenib alone is allowed in the relapsed/refractory cohort * PHASE 2 ONLY: No prior HCL-directed treatment for front-line cohort. The design of this cohort is such that the patients will need to be treatment naïve * Age ≥ 18 years. Because no dosing or adverse event (AE) data are currently available on the use of tovorafenib (DAY101) or cladribine in combination with rituximab in patients \< 18 years of age, children are excluded from this study * Patients must meet indications for treatment of cHCL: * Absolute neutrophil count \< 1,000/mcL * Platelets \< 100,000/mcL * Hemoglobin \< 10 g/dL * Recurrent infections * Symptomatic and/or progressive extramedullary disease including lymph nodes and bone lesions * Progressive or symptomatic splenomegaly or hepatomegaly * Disease-related constitutional symptoms consisting of unexplained weight loss exceeding 10% body weight during the preceding 6 months, Cancer Therapy Evaluation Program (CTEP) active version of the Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or 3 fatigue, and/or fever \> 100.5 F or night sweats for \> 2 weeks without evidence of active infection * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%); ECOG performance status \> 2 (Karnofsky \< 60%) will be allowed if considered due to HCL * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x institutional ULN (unless related to Gilbert's disease or HCL; patients with documented Gilbert's disease may be enrolled with sponsor approval provided total bilirubin is ≤ 2.0 x ULN) * Creatinine clearance (ClCr) ≥ 30 mL/min * 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 for \> 6 months * 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 * Electrocardiogram (ECG) without evidence of clinically significant ventricular arrhythmias or ischemia as determined by the investigator and a rate-corrected QT interval (QTc, Bazett's formula) of \< 480 msec * The effects of tovorafenib (DAY101), cladribine, and rituximab on the developing human fetus are unknown. For this reason and because BRAF kinase inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential (WOCBP) and men must agree to use two forms of adequate contraception (including a highly effective birth control method in addition to a barrier method) during treatment prior to study entry and for the duration of study treatment participation and 12 months after the last dose of the study medication * WOCBP should use effective non-hormonal contraception during treatment and for 12 months after the last dose of the study medication. 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. For male patients with a female partner of childbearing potential, a condom should be used for contraception in addition to one of the highly effective contraception methods prior to the study, for the duration of study treatment, and 12 months after the last dose of the study medication. Male patients must not father a child or donate sperm while participating in this study * Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives (LARs) may sign and give informed consent on behalf of study participants Exclusion Criteria: * Central nervous system (CNS) involvement with HCL is very rare, and therefore the biology of the disease in patients with CNS involvement may not be representative of the disease under study as a whole. Patients with treated brain metastases are eligible if follow-up brain imaging after CNS-directed therapy shows no evidence of progression * Patients with HCL who are BRAF V600E mutation negative and those with the variant HCL * Patients with platelets \< 50,000/mCL * Patients on warfarin and direct oral anticoagulants (due to risk of bleeding) * Patients who have not recovered from AEs as a result of prior anti-cancer therapy (i.e., have residual toxicities \> grade 1), with the exception of alopecia * Patients who are receiving any other investigational agents * Patients who are receiving strong CYP2C8 inhibitors, inducers, and breast cancer resistance protein (BCRP) substrates with narrow therapeutic index * Patients who are pregnant, breastfeeding, and/or unwilling to use adequate contraception during the study period and for 12 months after completion of the study * Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to tovorafenib (DAY101) or other agents used in the study, including those with a previous history of severe infusion-related reaction (anaphylaxis) with rituximab administration * Patients with known hypersensitivity to any of the study drugs * Patients with an inability to swallow oral medications or with gastrointestinal impairment * Live or live-attenuated vaccines within 28 days of randomization * Patients with uncontrolled intercurrent illness or any other significant condition(s) that would make participation in this protocol unreasonably hazardous * Pregnant women are excluded from this study because tovorafenib (DAY101) is a BRAF kinase inhibitor agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for AEs in nursing infants secondary to treatment of the mother with tovorafenib (DAY101), breastfeeding should be discontinued if the mother is treated with tovorafenib (DAY101). These potential risks may also apply to other agents used in this study