But, you can always open member's profile, at top select tab 'Visitor Messages' and post any message you like, and as many as you like.
Without any limit.

For example, to clean up PM Inbox.

There is no limit for this kind of messages.
And also, that member gets notification about received message.

As you can also post a message in your own profile, it is possible to have complete conversations this way.
Just open my profile [Only registered and activated users can see links. ] and then tab 'Visitor Messages'