環境は MySQL 5.7
値が null のレコードを検索するSELECT data FROM test WHERE JSON_EXTRACT(data, "$.value") = CAST('null' AS JSON);
+-----------------+
| data |
+-----------------+
| {"value": null} |
+-----------------+
値が 空配列 のレコードを検索する
SELECT data FROM test WHERE JSON_EXTRACT(data, "$.value") = JSON_ARRAY();
+---------------+
| data |
+---------------+
| {"value": []} |
+---------------+
https://dev.mysql.com/doc/refman/5.7/en/json-creation-functions.html#function_json-object
https://dev.mysql.com/doc/refman/5.7/en/json-search-functions.html#function_json-extract
https://dev.mysql.com/doc/refman/5.7/en/json.html