Você deve ser capaz de usar um LEFT JOIN para conseguir isso.
SELECT a.id AS stock, COALESCE(b.quanitity,0), b.product_id, a.name AS stock_fullname
FROM a
LEFT JOIN b
ON a.id = b.stock_id
AND b.product_id = 13
SELECT a.id AS stock, COALESCE(b.quanitity,0), b.product_id, a.name AS stock_fullname
FROM a
LEFT JOIN b
ON a.id = b.stock_id
AND b.product_id = 13
