Rituximab+ Zanubrutinib for Patients With Hairy Cell Leukemia and Hairy Cell Variant

Inclusion Criteria:• Histologically confirmed diagnosis of hairy cell leukemia or variant according to World Health Organization (WHO) criteria with any of the following indications for therapy: * Hemoglobin \< 11 g/dL, Platelet count \< 100,000/mL, Absolute neutrophil count \< 1,000/mL * Progressive or symptomatic splenomegaly or hepatomegaly or Enlarging lymphadenopathy \>= 2 cm * Disease related constitutional symptoms consisting of unexplained weight loss exceeding 10% of body weight over 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, fevers \> 100.5 degrees Fahrenheit (F) or night sweats for greater than 2 weeks without evidence of infection • Patients may receive therapy under the following conditions: * After at least 1 prior purine nucleoside analog-containing regimen (fludarabine, pentostatin, or cladribine), or * Relapsed or de novo disease if deemed medically unfit for therapy with a purine nucleoside analog * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Creatinine =\< 2.0 mg/dL, and/or creatinine clearance (estimated glomerular filtration rate \[GFR\] \[Cockcroft-Gault\]) \>= 30 mL/min (Annex 1) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (unless disease related or due to Gilbert's disease) or Aspartate aminotransferase (AST) =\< 3.0 x ULN (unless disease related) * The effects of BTKi on the developing human fetus are unknown; for this reason, and because tyrosine kinase inhibitors may be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry; female patients who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; or history of hysterectomy; or history of bilateral tubal ligation; or history of bilateral oophorectomy); female patients of childbearing potential must have a negative serum pregnancy test upon study entry; male and female patients who agree to use highly effective methods of birth control (e.g., condoms, implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], complete sexual abstinence, or sterilized partner) during the period of therapy and for 90 days after the last dose of study drug; 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 * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Prior exposure to a Bruton's tyrosine kinase (BTK) inhibitor * Zanubrutinib is extensively metabolized by CYP3A4/5; patients who received a strong cytochrome P450 (CYP) 3A inhibitor within 7 days prior to the first dose of Zanubrutinib or patients who require continuous treatment with a strong CYP3A inhibitor; therefore, any medications or substances that are strong inhibitors of CYP3A4/5 should be discontinued if possible; Zanubrutinib dose modification to 80 mg QD is recommended when patients are on strong CYP3A inhibitors; because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list; medical reference texts such as the Physicians' Desk Reference may also provide this information; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; recent infections requiring systemic treatment need to have completed therapy \> 14 days before the first dose of study drug * Pregnant or breast-feeding or intending to become pregnant during the study * Have had chemotherapy (including purine analogs), rituximab, and other investigational agents within four weeks prior to entering the study. * Invasive malignancy within the past 2 years prior to first study drug administration, except for adequately treated (with curative intent) basal or squamous cell carcinoma, melanoma, in situ carcinoma of the cervix, in situ ductal adenocarcinoma of the breast, in situ prostate cancer, or limited stage bladder cancer or other cancers from which the patient has been disease-free for at least 2 years * Active HIV, hepatitis B and hepatitis C or any clinically significant history of liver disease. Hepatitis B prior infection is not a contraindication though will require therapy. * Known hypersensitivity to any of the study drugs * Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * Patient is unable to swallow capsules, or has disease significantly affecting gastrointestinal function or resection of the stomach or small bowel, or symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction * History of intracranial hemorrhage within 6 months prior to enrollment