Update with subselect on the same table.

update_select.sql

UPDATE
    product
SET
    product_active = 0, product_date_deleted = NOW()
WHERE product_id IN (SELECT product_id
    FROM (SELECT
            product.product_id
        FROM
            product
        LEFT JOIN
            product_image ON (product.product_id = product_image.product_id AND product.product_date_deleted IS NULL)
        GROUP BY
            product.product_id
        HAVING
            COUNT(product_image.image_id) = 0) product_copy );