Could a cancer drug tame a blood disorder?

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * Eastern Cooperative Oncology Group (ECOG) =\< 2 * "Warm" or "cold" AIHA in patients with CLL, relapsed/refractory (RR) after first line treatment with oral prednisone (with or without rituximab), defined as: * Anemia (hemoglobin \[Hgb\] =\< 10 g/dL; or Hgb \> 10 g/dL dependent on transfusions or maintenance therapy (rituximab, cyclosporin, etc) to maintain this level of hemoglobin, and * Laboratory evidence of hemolysis - presence of 3 of 4 markers (increased reticulocyte count, increased indirect bilirubin, increased lactate dehydrogenase, absent haptoglobin) * Positive direct antiglobulin test (DAT) (score \>= 1+) - either immunoglobulin G (IgG) DAT, C3 DAT, or both. Eligibility of patients with Coombs-negative AIHA should be confirmed by the trial investigator at each respective study site * Histologically or flow cytometry confirmed diagnosis of CLL/small lymphocytic lymphoma (SLL) * Participant must be able to swallow tablets or capsules * Absolute neutrophil count (ANC) \>= 500/mm\^3 unless due to disease involvement in the bone marrow or autoimmune neutropenia (within 30 days prior to day 1 of protocol therapy) * Platelets \>= 30,000/mm\^3 unless due to disease involvement in the bone marrow or autoimmune thrombocytopenia (Evans syndrome) (within 30 days prior to day 1 of protocol therapy) * Direct bilirubin =\< 3.0 x upper limit of normal (ULN) (within 30 days prior to day 1 of protocol therapy) * Aspartate aminotransferase (AST) =\< 3.0 x ULN (within 30 days prior to day 1 of protocol therapy) * Alanine aminotransferase (ALT) =\< 3.0 x ULN (within 30 days prior to day 1 of protocol therapy) * Creatinine clearance of \>= 30 mL/min per 24 hour urine test or the Cockcroft-Gault formula (within 30 days prior to day 1 of protocol therapy) * If not receiving anticoagulants: International normalized ratio (INR) OR prothrombin (prothrombin time \[PT\]) \< 2 x ULN (within 30 days prior to day 1 of protocol therapy). If on anticoagulant therapy: PT must be within therapeutic range of intended use of anticoagulants (within 30 days prior to day 1 of protocol therapy) * If not receiving anticoagulants: Activated partial thromboplastin time (aPTT) \< 2 x ULN (within 30 days prior to day 1 of protocol therapy). If on anticoagulant therapy: aPTT must be within therapeutic range of intended use of anticoagulants (within 30 days prior to day 1 of protocol therapy) * Seronegative for human immunodeficiency virus (HIV) Ag/Ab combo, hepatitis C virus (HCV), active hepatitis B virus (HBV) (surface antigen negative), and syphilis (rapid plasma reagin \[RPR\]) (within 30 days prior to day 1 of protocol therapy) * If positive, hepatitis C ribonucleic acid (RNA) quantitation must be performed * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test within the screening window prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Agreement by females of childbearing potential to use highly effective methods of birth control or abstain from heterosexual activity starting with the first dose of study therapy through 2 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: * Therapeutic anticancer antibodies within 3 weeks * Radio- or toxin-immunoconjugates within 10 weeks * BH3-mimetic venetoclax, PI3K inhibitors and other "targeted" therapy- within 6 half-lives * Ibrutinib, acalabrutinib or another BTK inhibitor within 12 months * Patients on stable chronic AIHA treatments are allowed provided the dose has not changed in the 4 weeks prior to enrollment * Allogeneic stem cell transplant within 1 year prior to day 1 of protocol therapy, or ongoing immunosuppressive therapy for chronic graft versus host disease (cGVHD) * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 21 days prior to day 1 of protocol therapy * Strong CYP3A4 inducers/ inhibitors. If the patient requires a strong CYP3A inhibitor/inducer, they should not be enrolled even if it could be held for 14 days before the first dose of study drug * Proton pump inhibitors (but patients who switch to H2-receptor antagonists or antacids are eligible for enrollment) * Chronic use of corticosteroids (\> 2 weeks) in excess of prednisone 60 mg/day or its equivalent within 4 weeks prior to start of study therapy. Rescue steroids are allowed during trial * Vitamin K antagonists * Known intolerance to acalabrutinib * History of bleeding disorders or with active bleeding * Patients with suspected or confirmed progressive multifocal leukoencephalopathy (PML) * Patients with history of stroke or intracranial hemorrhage within 6 months * Inadequate recovery from adverse events related to prior therapy to grade 1 or baseline (excluding grade 2 alopecia and neuropathy) * Active uncontrolled infection * Known history of immunodeficiency virus (HIV) infection * Subjects who have an undetectable or unquantifiable HIV viral load with CD4 \> 300 and are on highly active antiretroviral therapy (HAART) medication are allowed. Testing to be done only in patients suspected of having infections or exposures * Active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV) * Participants who are hepatitis B core antibody (anti-HBc) positive and who are surface antigen negative will need to have a negative polymerase chain reaction (PCR). Those who are hepatitis B surface antigen (HbsAg) positive or hepatitis B PCR positive will be excluded. Note that intravenous immunoglobulin therapy (IVIG) administration may lead to positive anti-HBc test result * Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded * Major surgery (requiring general anesthesia) within 28 days prior to initiation of therapy * Has difficulty with or is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication * History of prior malignancy except: * Malignancy treated with curative intent and no known active disease present for \>= 2 years prior to initiation of therapy on current study * Adequately treated non-melanoma skin cancer or lentigo maligna (melanoma in situ) without evidence of disease * Adequately treated in situ carcinomas (e.g., breast, cervical, esophageal, etc.) without evidence of disease * Asymptomatic prostate cancer managed with "watch and wait" strategy * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification, or left ventricular ejection fraction (LVEF) =\< 40% * Psychiatric illness/social situations that would limit compliance with study requirements * Participant is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial * 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