Facebook has been holding out on you.
See, when a friend sends you a private message, you get a notification in your Messages feed (which, if you're like some people I know, you never bother to check). Depending on your settings, you may also get an email.
However, what happens when someone you don't know sends you a message on Facebook? The network stays surprisingly mum about it: You get no notification whatsoever. Instead, these messages get routed into a second inbox called Other. And there they sit, easily overlooked -- unless you make an effort to access that inbox from time to time.
Fortunately, it's not hard to find -- if you're accessing Facebook in your browser. The mobile apps offer no way to open your Other folder.
In your browser, however, look to the lefthand toolbar. You should see a link labeled Messages:
Click it and you'll see your primary inbox. But then if you click Other, you'll find whatever messages have been directed there:
You can also click the Messages icon in the top toolbar, then click Other in the drop-down window that appears:
Once you're reading a message (by accessing the full Other inbox, as described above), you'll see an Actions button. Click to move the note to your primary inbox, open a chat with the sender, and so on:
It's just my two cents, but Facebook needs to do a better job notifying users when something "other" is going on.