I have six PMs that I have sent to members of this forum (some of which date back to 2015) that have not been picked up - they're still sitting my my out-basket. I suspect that a member doesn't even know that a message is there as they haven't logged in, as they haven't enabled automatic email notification that a message is waiting for them.
Just a quick refresher on how to enable these email notifications:
1. After you Login, click and hold on your name in the upper right-hand corner.
2. Select User Control Panel
3. Select Edit Global Settings
4. If you click YES on "Allow users to send you private messages" means that someone can communicate with you other than creating a post in a thread.
I wouldn't worry about being overwhelmed by emails because, even as a moderator, I get maybe one notification a month on average, and that usually being a spam flag.