Allow special DMs from users with administrator

I am an admin on a server and have talked to other mods who have had this happen on their servers.
 Sometimes a user may leave do to an unfortunate circumstance.
And, at the moment, the only way to contact a user is if you are friends or you happen to be in another server. If neither of these options are available, your only option to contact them is to send a friend request and hope that they notice that you are from the server they left.

It would be nice if the admins of the server could open up a DSM(Direct Server Message) to someone who has left the server as a representative of the server. 
The difference between a regular DM and a DSM is that the server itself is sending the DM and, if blocked, no admin from the server would be able to send messages. Also the DSM is accessible to all server admins.

A DSM would mainly be used as a conversation between admins and a previous server member to apologize to the user and allow them to contact them after they have left.