Every account on Facebook has two inboxes, one of them in which you can view all messages and chat history from your friends and another inbox called “Other” where all the messages from pages you have liked or even from people you are not yet friends with. This may be missed by some users on Facebook.
There are 2 inboxes in every Facebook account. To access this hidden inbox, go to the Messages tab on the homepage. Under the messages panel, you will see a tab called “Other”. Here you will see all messages that have been sent to you by pages that you have like or even by people who you are not friends with. This inbox is usually useless filled with updates from pages you have like or games you have played on Facebook. But this is not always the case. Sometimes, a friend or an acquaintance who is not your friend may send you an important message. Since that person is not your friend on Facebook, their message will be sent to your “Other Messages” panel. You will only be able to view this message by accessing the other inbox manually.
There is presently no way to tweak this non-notifying function of Facebook when you receive a message from an anonymous user. So, you have to make sure to check this out from time to time.