Explain handling an exception inside a loop so processing continues

If the EXCEPTION section is on the outer block, the first error ends the whole loop. Put a nested block around the per-iteration work: its handler catches the failure for that row, records it, and control returns to the loop for the next iteration. This is the row-by-row 'reject and continue' pattern. For bulk DML the equivalent is FORALL ... SAVE EXCEPTIONS. Be deliberate about whether a partial run should COMMIT.

FOR r IN (SELECT * FROM staging_invoices) LOOP
  BEGIN
    load_one_invoice(r);                 -- may raise
  EXCEPTION
    WHEN OTHERS THEN
      INSERT INTO staging_errors(row_id, err, logged_at)
      VALUES (r.row_id, SQLERRM, SYSTIMESTAMP);
  END;
END LOOP;
COMMIT;