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.
Update: Facebook recently phased out the Other folder in favor of something called Message Requests. In a desktop browser, it functions more or less the same as Other, described below.
If you have the Facebook Messenger app, however, you'll see Message Requests (i.e., messages from people you don't know) inline with other messages. Here's some info on the roll out of this new feature.
In your browser, however, look to the left-hand 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.