The most obvious way to monetise facebook is to me some kind of job advertising platform. They have all this data on people, like whether they're students, where and studying what, etc. Companies looking to recruit could buy job ad placements based on those criteria. (e.g. show this job to final-year CompSci BSc students at Cambridge and Oxford) The more specific and popular, the more expensive.
I suppose it's possible that they've explored it but there isn't a market for this. I guess with the job market right now might not be the best time for that kind of feature - on the other hand there are probably lots of users who would use it.
See something like this makes sense for LinkedIn, who unless I am mistaken is already doing it well and making money off it. If you take a look at the Facebook Marketplace, you will find it is pretty diluted with spam and other junk listings (Last time I checked this was 6 months ago so I may be wrong now.)
If you look at who's using Facebook, most of them are using it to play games and spread PIRATE BOOTY not search for jobs. Although there is a small subset of users who would use it, I don't think it would be enough to monetize.
Depends how small the subset is. They have ~150 million users and should break 200 million this year. Several services serving small subsets could be enough to make a profit.
I suppose it's possible that they've explored it but there isn't a market for this. I guess with the job market right now might not be the best time for that kind of feature - on the other hand there are probably lots of users who would use it.