I think it's time we discussed Facebook's "Other" folder. Introduced in 2011, the folder holds your spam messages, or what Facebook determines is spam. Per Facebook, it is, "where you'll find messages and emails that have been filtered out of your inbox."
You can access the folder by going to your messages—either on its own page, or directly from your news feed in the taskbar—and clicking "other." It is next to the inbox title on both pages. You can change what gets through to your inbox, and what gets sorted into your other folder, by adjusting your filter preferences.
These are your options:
It's a good idea to keep an eye on your other folder. While messages that are sent to your Facebook inbox will likely come to your e-mail's inbox as well, your other messages will not. There will not be notifications, and the messages will be lonely and dormant.
This has also been, from my perspective, an opportunity for Facebook to plunder your dollars. Sending messages to the inbox of people who are not your friends will cost $1. Again: to send the messages to the non-friend's inbox, you'll have to pay $1. Sending the message for free will dump your missive into the other folder. Here is evidence, because I find the affair shocking:
What is the "Other" folder in my messages?, Facebook help
Facebook tests $1 fee for messages for non-friends, Yahoo News
The "Other" Facebook inbox you didn't know you had, PC World