I'm not sure if in a single query you can achieve what you need.
The following stored procedure, perhaps, can give you some ideas (stored procedure works for MariaDB and for MySQL):
> DROP PROCEDURE IF EXISTS `JSON_query_based_on_key`;
Query OK, 0 rows affected (0.01 sec)
> DELIMITER //
> CREATE PROCEDURE `JSON_query_based_on_key`(
-> `json` TEXT,
-> `key` VARCHAR(5)
-> )
-> BEGIN
-> DECLARE `sub_things_current` INT
-> DEFAULT JSON_LENGTH(`json`, '$.thing.sub_things') - 1;
->
-> WHILE (`sub_things_current` > -1) DO
-> IF NOT JSON_CONTAINS_PATH(
-> `json`,
-> 'one',
-> CONCAT('$.thing.sub_things[', `sub_things_current`, '].attribute[*]."', `key`, '"')
-> ) THEN
-> SET `json` := JSON_REMOVE(
-> `json`,
-> CONCAT('$.thing.sub_things[', `sub_things_current`, ']'));
-> END IF;
-> SET `sub_things_current` := `sub_things_current` - 1;
-> END WHILE;
->
-> SELECT JSON_EXTRACT(`json`, '$.thing');
-> END//
Query OK, 0 rows affected (0.00 sec)
> DELIMITER ;
> CALL `JSON_query_based_on_key`('{
'> "thing": {
'> "sub_things": [
'> {
'> "attribute": [
'> { "1": 40 },
'> { "5": 25 },
'> { "13": 35 }
'> ]
'> },
'> {
'> "attribute": [
'> { "2": 50 },
'> { "7": 50 }
'> ]
'> }
'> ]
'> }
'> }', '13');
+---------------------------------------------------------------------+
| JSON_EXTRACT(`json`, '$.thing') |
+---------------------------------------------------------------------+
| {"sub_things": [{"attribute": [{"1": 40}, {"5": 25}, {"13": 35}]}]} |
+---------------------------------------------------------------------+
1 row in set (0.00 sec)
Query OK, 0 rows affected (0.00 sec)
Modify the code as you need it.
See db<>fiddle for MariaDB (10.2.6) and db-fiddle for MySQL (5.7.17).
JSONis not necessarily the best design of the schema.