After doing CTE Select Order By and then Update, Update results are not ordered the same (TSQL) - tsql

Question

The code is roughly like this:
WITH cte AS
(
SELECT TOP 4 id, due_date, check
FROM table_a a
INNER JOIN table_b b ON a.linkid = b.linkid
WHERE
b.status = 1
AND due_date > GetDate()
ORDER BY due_date, id
)
UPDATE cte
SET check = 1
OUTPUT
INSERTED.id,
INSERTED.due_date
Note: the actual data has same due_date.
When I ran the SELECT statement only inside the cte, I could get the result, for ex: 1, 2, 3, 4.
But after the UPDATE statement, the updated results are: 4, 1, 2, 3
Why is this (order-change) happening?
How to keep or re-order the results back to 1,2,3,4 in this same 1 query?

Answer 1

In MSDN https://msdn.microsoft.com/pl-pl/library/ms177564(v=sql.110).aspx you can read that
There is no guarantee that the order in which the changes are applied
to the table and the order in which the rows are inserted into the
output table or table variable will correspond.
Thats mean you can't solve your problem with only one query. But you still can use one batch to do what you need. Because your output don't guarantee the order then you have to save it in another table and order it after update. This code will return your output values in order that you assume:
declare #outputTable table( id int, due_date date);
with cte as (
select top 4 id, due_date, check
from table_a a
inner join table_b b on a.linkid = b.linkid
where b.status = 1
and due_date > GetDate()
order by due_date, id
)
update cte
set check = 1
output inserted.id, inserted.due_date
into #outputTable;
select *
from #outputTable
order by due_date, id;