By default, anyone on Facebook can send you a message, and if you set up a Facebook email address, anyone outside of Facebook can send you email. Email from friends and their friends goes directly to your main Messages folder, and everything else goes to the Other folder within your Messages. If an email appears to be from someone you know but we are unable to confirm the sender's address, you will still receive the message, but it will include a warning.
If you’d like to modify who can send you Facebook messages and email:
Click the account menu at the top right of any Facebook page and choose Privacy Settings.
Next to the How You Connect heading, click Edit Settings.
Select your preference from the dropdown menu next to “Who can send you messages on Facebook?”
Only emails from people that fall within the message privacy setting you choose will be delivered to your Facebook Messages. For example, if you select the "Friends Only" setting, you will not receive messages from email addresses that we can't confirm as belonging to one of your friends. Instead, those senders will receive automatic bounce-back replies.
Note: Changes to the "Who can message me" privacy setting may take up to 24 hours to take effect.