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)

Inclusion Criteria:

Key Inclusion Criteria:

* 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:

Key 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.