Usually mail will defer in this case. Local mail still should be deliverable, maybe. NIS is unavailable. This is more serious, since our MTA won't be able to look up any local users. Exim in this case sends temporary failure messages to all incoming mail - the sending MTA should then retry the delivery at set repeating times.
Users can often break their own mail.
It ought to be okay for a .forward to be 600. If it's 666 or even 777, exim will refuse to deliver mail to this address. Because anyone on our system could edit this file and put in a nefarious pipe command. This results in a recursive mail loop. In cases like this, you can backup their .forward, put a proper .forward in place, and send them mail explaining what you did and why.