Stačí definovat druhý dotaz, který vytvoří prázdné řádky, které potřebujete, a sjednotit je dohromady.
SELECT ROW_NUMBER() OVER(PARTITION BY family_id ORDER BY family_id) AS rowNum,
full_name as name,
family_id
FROM tbl_person
UNION ALL
SELECT n.N AS rowNum,
NULL AS name,
p.family_id
FROM (SELECT family_id, COUNT(*) family_count FROM tbl_person group by family_id) p
INNER JOIN (
SELECT 1 AS N
UNION ALL SELECT 2
UNION ALL SELECT 3
UNION ALL SELECT 4
) n
ON n.n > p.family_count
ORDER BY family_id,
rowNum,
name;