EAV - Add rows with null value if row does not exist - mysql

Question

I have the following table storing data in the EAV model:
+-------------+---------+------+-----+---------+-------+
| Field | Type | Null | Key | Default | Extra |
+-------------+---------+------+-----+---------+-------+
| user_id | int(11) | NO | MUL | NULL | |
| question_id | int(11) | NO | MUL | NULL | |
| answer | blob | YES | | NULL | |
+-------------+---------+------+-----+---------+-------+
With a table to hold the different types of question:
+----------+---------+------+-----+---------+----------------+
| Field | Type | Null | Key | Default | Extra |
+----------+---------+------+-----+---------+----------------+
| id | int(11) | NO | PRI | NULL | auto_increment |
| question | blob | YES | | NULL | |
+----------+---------+------+-----+---------+----------------+
As well as a users table:
+------------------+--------------+------+-----+---------+----------------+
| Field | Type | Null | Key | Default | Extra |
+------------------+--------------+------+-----+---------+----------------+
| id | int(11) | NO | PRI | NULL | auto_increment |
| user_name | varchar(128) | YES | | NULL | |
+------------------+--------------+------+-----+---------+----------------+
How would I write a query to insert a row with a null value for answer for each question_id that each user does not currently have a row for?
For example, if I have question_ids 1,2,3,4 and my table storing data looks like:
+--------------+---------------+--------+
| user_id | question_id | answer |
+--------------+---------+-----+--------+
| 1 | 1 | example|
| 1 | 3 | example|
| 1 | 4 | example|
+--------------+---------+-----+--------+
I want to insert a row that looks like :
+--------------+---------------+--------+
| user_id | question_id | answer |
+--------------+---------+-----+--------+
| 1 | 2 | NULL |
+--------------+---------+-----+--------+
I tried something like this:
INSERT INTO profile_answers
(
user_id,
question_id,
answer
)
SELECT
id,
profile_answers.question_id,
null
FROM users
LEFT JOIN profile_answers ON profile_answers.user_id = users.id
WHERE NOT EXISTS (
SELECT answer
FROM profile_answers
WHERE user_id = id
AND question_id IN (
SELECT GROUP_CONCAT(id SEPARATOR ',') FROM profile_questions
)
)
But I ended up inserting rows with a question id of 0.

Answer 1

I've given this some thought, but I couldn't find anything better than using a cartesian product between users and questions, and a filtering subquery:
SELECT u.id, q.id
FROM users u,
questions q
WHERE NOT EXISTS(
SELECT *
FROM profile_answers a
WHERE a.question_id = q.id AND a.user_id = u.id
);
Demo