Interferon-Beta-1a (FP-1201) to Prevent Toxicities After CD19-Directed CAR T-Cell Therapy

Inclusion Criteria: * Participants must be 18 years of age or older * Karnofsky performance status of \>= 60% * Participants eligible for treatment with axi-cel or brexu-cel * Negative serum pregnancy test within 2 weeks of enrollment for women of childbearing potential, defined as those who have not been surgically sterilized or who have not been free of menses for at least 1 year * Fertile male and female participants must be willing to use an effective contraceptive method before, during, and for at least 4 months after the last dose of FP-1201 * Ability to understand and provide informed consent Exclusion Criteria: * Known hypersensitivity to natural or recombinant interferon beta, albumin or any other component of the formulation * Estimated creatinine clearance (Cockcroft and Gault) =\< 60 mL/min * Significant proteinuria defined as 2+ or 3+ proteinuria or urinary protein \>= 1g/24h * Severe hepatic dysfunction defined as group C of the National Cancer Institute Organ Dysfunction Working Group hepatic impairment criteria (total bilirubin \> 3x upper limit of normal \[ULN\] with any aspartate aminotransferase \[AST\] or alanine transaminase \[AL\]T value), or AST or ALT \> 3x ULN, unless due to malignancy or Gilbert's syndrome in the opinion of the principal investigator (PI) or designee * Participants with clinically significant pulmonary dysfunction, as determined by medical history and physical exam should undergo pulmonary function testing, as clinically indicated. Those with an forced expiratory volume in the first second (FEV1) of \< 50 % of predicted or diffusing capacity of the lungs for carbon monoxide (DLCO) (corrected) \< 40% will be excluded * Significant cardiovascular abnormalities as defined by any one of the following: * New York Heart Association (NYHA) class III or IV congestive heart failure, clinically significant hypotension * Uncontrolled symptomatic coronary artery disease, or a documented ejection fraction of \< 35% * Uncontrolled serious and active infection * Corticosteroid use (\> 20mg/day of prednisone, or equivalent) within 7 days prior to first FP-1201 administration