Facebook Messenger – Meaning of Phone Icon

No, it isn't possible to know if someone if online and has just set their status as offline. It may arise a privacy concern.

But there's a way to know if someone is online or not by checking their profile, check if they recently liked status, page or anything which can indicate that they are active. But it won't always work.

Update: There's another trick which can tell you if an user is active or not. Setup a group chat on Facebook by sending a message to more than one friend (also add the friends you want to know active status of) and then send a random message, now when someone in the group chat will see the message, there will be a notification like Seen by [name] and if your friends see the message, the notification will be shown for them too.

Your friend has completely logged out of Facebook on his or her mobile device and has chat set to "off" on their computer. FYI: This does not mean he or she is truly offline. He or she can still access Facebook via their web connection without any indication of activity or of a time stamp. Extensive personal experience avoiding a stalker has led me to this solution.