Are you using any control panel? Control panels like Cpanel has monitoring systems to restart a service if it is not running. If you are using Cpanel go to WHM >> Service Configuration >> Service Manager and disable exim if you don't want to get it restarted automatically.
And in Cpanel servers, you can prevent mails from going to a particular domain using antivirus.exim file.
In this file you can see a section like this.
if $header_from: contains "@sexyfun.net"
fail text "This message has been rejected since it has\n\
the signature of a known virus in the header."
Now you can add a different section for $header_to with that domain.
Or you can use an iptables rule to prevent outgoing connections through port 25 for that IP.
Shoot if you have any questions.