I should have seen this coming. Recently, Facebook conducted an experiment to "test the usefulness of economic signals to determine relevance." I genuinely love the language chosen here; it means that users who are (were?) part of the test get the option to pay to have a message reach the recipient's main inbox. I don't know what the cost per message was for those users in the experiment, but AllThingsD's sources say a dollar, and that "Facebook will tinker with the fee over time." Facebook wrote, "in this test, the number of messages a person can have routed from their Other folder to their Inbox will be limited to a maximum of one per week." (I assume Facebook is referring to the recipient's Other folder and the recipient's Inbox.)
The Other folder was introduced in 2010; it was one of many changes to the Facebook messaging product, all of which I hated (I don't have a decently written post to link back to with an explanation). It had a few issues. Pages you had Liked from then on could not reach your main inbox, at least by default. I consider this to be a problem because you might want content from a Page that you Like, including in your inbox. There isn't an adequate solution to this problem based on already-in-place signals, but if Facebook were to have Follow buttons on Pages separate from Like, which the company disappointingly has no plans for, following a Page would be that (adequate, not perfect) signal. The other thing that resulted from the Other folder's introduction was that if you were sending a message to someone, that message would either go to that person's main inbox or to that person's Other folder. What Facebook might call social signals would determine to which folder a message would be delivered. I think that it would depend on a user's settings whether he would receive messages from people who were not friends with him, though I believe the default was to have at least people who were neither friends nor friends of friends filtered into his Other folder.
The black hole that is the Other folder
When a message lands into the Other folder, the recipient is not notified, at least, not in the normal way. One way that Facebook notified the recipient when this system was first put into place was a new message counter next to the Other folder. And where could a user find his Other folder? Under "Messages" in Facebook's left sidebar, but only when he clicked "Messages" and the counter certainly wasn't red. I'm not sure whether this counter was visible enough even when it was visible. But it was downright invisible unless you clicked on Messages (or got a new message notification and followed it to read your new message; I believe then it would be not invisible). This would not be good for a user who visited the messages section of Facebook infrequently, or saw the Other folder as akin to a spam folder and not where valuable messages get hidden. By the way, in my opinion, the Other folder is more visible in Facebook's current design, but it is still invisible unless you click "Messages" or are in the "Messages" section of Facebook.
The latest news on Messages
Here's Facebook's post about how Message filtering options have changed. It seems from this post that there were some half-decent options for undoing some of Facebook's dual-inbox shenanigans. Interested? Sorry, those options are gone now; in their place, Basic Filtering and Strict Filtering. Facebook didn't post details on the "economic signals" test.
Better than a guarantee your message won't be read
The Other folder is as inconvenient/detrimental to the sender as it is to the recipient. It's close to a guarantee your message won't be read. And the worst part: there's no warning that your message is just going to go to the Other folder (that I know of). That's a problem. We may see a solution though, and that will be in the form of "economic signals," like it or not. Because the only way a toll will be a relevant signal (and the only way it will yield much revenue) is if when the rerouting option applies, it presents itself with some kind of explanation of what the Other folder is and why you don't want your message to land there. Unless Facebook is implementing this without a free option and with no explanation of why there's a charge, which I somehow doubt. It is yet to be seen if Facebook will make the charge a "feature."
It wouldn't be a nice feature. And if Facebook simply had spam filtering, instead of this weird filtering system that weeds out the could-be-extremely-important but don't worry because that stuff isn't "meaningful," this wouldn't be necessary. Provided it were good, no,—excellent—spam filtering. But that wouldn't make any money; would it? Perhaps what Facebook was thinking when they introduced a dual-inbox in 2010? Ha, but I don't think Facebook's smart enough to think of that.
The one per week limit is ridiculous. From what I can make of Facebook's post, it's one rerouted message per week for the recipient (from any number of senders?), i.e. if you're a sender and your intended recipient has had a message rerouted earlier in the week, Facebook will tell you you have to wait until next week to get in touch. That's my best guess as to what the limit means. If you're very famous and people are paying to message you all the time, perhaps you should have your profile set to not be searchable.