A Study to Assess Adverse Events, How the Drug Moves Through the Body and Effectiveness of Intravenous Infusions and Subcutaneous Injections of ABBV-519 in Adult Participants With Systemic Lupus Erythematosus (SLE) or Rheumatoid Arthritis (RA)

* Individuals between 18 and 75 years of age inclusive at the time of Screening. * Minimum baseline B-cell count of 50 cells/mcL. Inclusion Criteria for SLE Participants: * Clinical diagnosis of SLE and fulfilling the 2019 EULAR/ACR classification criteria. * Positive ANA ≥ 1:80 and the presence of at least one of the following autoantibodies above the upper limit of normal (ULN): anti-double-stranded DNA (dsDNA), anti-Smith (Sm), anti-ribonucleoprotein (RNP), or anti-Sjogren's syndrome antigen A (SSA). * Hybrid Systemic Lupus Erythematosus Disease Activity Index (hSLEDAI) score of ≥ 4 (excluding anti-dsDNA and C3/C4). Lupus headache or organic brain syndrome do not count towards the hSLEDAI points required for eligibility. * Participants must have an inadequate response to ≥ 1 immunosuppressant therapies, used for at least 3 months. Inclusion Criteria for RA Participants: * Clinical diagnosis of RA and fulfilling the 2010 ACR/EULAR classification criteria for RA. * Presence of rheumatoid factor (RF) or anti-citrullinated peptide antibodies (ACPA) above the ULN. * Presence of at least 6 swollen and 6 tender joints * High-sensitivity C-reactive protein (hs-CRP) ≥ 3 mg/L. * Failed at least 1 conventional synthetic disease-modifying antirheumatic drug (DMARD) and ≥ 1 biological or targeted DMARDs of different classes. Exclusion Criteria:

* Participants with a history of infection. * Participants with uncontrolled hypertension Exclusion for SLE Participants: * Active neuropsychiatric SLE, or signs or symptoms of neuropsychiatric SLE within the 6 months prior to Screening (lupus headache permissible). \- Unstable or progressive glomerulonephritis (active class III or IV). * SLE overlap syndromes including, but not limited to RA, Sjogren's disease (SjD), SSc, polymyositis, dermatomyositis, or mixed connective tissue disease. Exclusion for RA Participants: \-- History of RA overlap syndromes, including but not limited to SLE, SjD, scleroderma, mixed connective tissue disorder or polymyositis.