In MySql you can't update a table if you have a subquery that references the same table, but you could sostitute the subquery with JOINS. I would do this, it's a trick but it works:
UPDATE
inbox inner join (select max(id) as maxid from inbox) mx on inbox.id = mx.maxid
SET inbox.`read` = 0
EDIT: I see you edited your question, so i have to edit my answer:
UPDATE
inbox
INNER JOIN (select max(inbox.id) as maxid
from
inbox inner join messages
on inbox.message_id = messages.id
where
messages.conversation_id=10
and inbox.user_id=1) mx
on inbox.id = mx.maxid
SET inbox.`read` = 0
Your subquery returns the maximum id based on the conversation_id
and the user_id
you want, then you join inbox
whith the maximum id to select just the row you want, and you can then update just that row.