Você pode usar a seguinte consulta:
SELECT pr.person_id AS [person.id], pr.person_name AS [person.name],
(
SELECT pt.pet_id AS id, pt.pet_name AS name
FROM @Pets pt WHERE pt.pet_owner=pr.person_id
FOR JSON PATH
) AS [person.pet]
FROM @Persons pr
FOR JSON PATH, ROOT('pet owners')
Para obter mais informações, consulte https://blogs.msdn.microsoft.com/sqlserverstorageengine/2015/10/09/returning-child-rows-formatted-as-json-in-sql-server-queries/