Facebook's Inbox was never well-publicized, new messages hidden in an "Other" inbox that was hidden unless you knew (and remembered to actually check it). New emails didn't result in notifications and were missing from the mobile apps.
The last message I see in that inbox (from a Facebook group/page I am a fan of) was from 2011.
This may have been a missed opportunity for Facebook (probably would be considered a "distraction") but also speaks to the strength of email as a stand-alone platform. Attempts to redefine or integrate email into something else is not an easy proposition.