Secondary Immune Deficiency

This is a prospective, multicenter, open-label, single-arm study to assess the efficacy, safety, and pharmacokinetics (PK) of IgPro20 in adults with hematologic malignancies treated with B-cell targeting Chimeric antigen receptor T-cell (CAR T-cell) and T-cell redirecting therapies (such as T-cell engager bispecific antibody \[TCE BsAb\] therapy). The primary objective is to demonstrate that true annualized rate of serious bacterial infection (SBIs) is less than (\<) 1.0. This study includes two cohorts: 1. Loading Cohort: Participants with serum immunoglobulin G (IgG) \< 500 milligrams per deciliter (mg/dL) at Screening, with or without ongoing immunoglobulin replacement therapy (IgRT) during Screening, who must have received five doses of IgPro20 during the Initial Treatment Period. 2. Maintenance-only Cohort: Participants with serum IgG greater than or equal to (≥) 500 mg/dL and ongoing IgRT at Screening, who must have received one dose of IgPro20 during the Initial Treatment Period.