I know I have explained this to several people and I know they CAN'T be the only ones that don't know about this, so I decided to make a blog post so I can just send people to it :)
When someone (page or person) PMs (private messages) you on facebook and they are not your friend it will not go into your messages inbox until you have replied back. I know several pages try and contact giveaway winners this way, and I know I would hate to miss winning something because I couldn't find their message. So here is the quick and easy way to find that message that they said they sent, but you can't locate in your inbox:
Step 1: On your home page in the upper left corner under your profile picture there is a navigation menu. You will want to click on the one that says "messages"
Step 2: After you do there will be another sub-category show up that says other. Click on "other" this is where those PMs from non-friend pages/people go. After you reply to the message it will then be moved to your inbox.
I hope this helps :)
Disclaimer: All posts and opinions are my own. They may not be the same as yours, but being individuals I can't please everybody. However this is my blog :P