If you're on the desktop browser version of Facebook, open the messages drop-down near the top-right corner, click "Message Requests," then click where it says "See filtered requests." If you're on the Facebook Messenger app, tap the Settings icon at the bottom, then tap the following: People > Message Requests > See filtered requests.
Yep, it's really that simple and you're going to kick yourself for never noticing it before. But brace yourself, folks, as there could be legit missed messages from distant acquaintances, people trying to contact you for business opportunities, or actual people asking you out on a date that you've now rudely ignored for months. Or your filtered requests are just a bunch of unintelligible spam messages, a zillion randos who just said "hi,' and if you're lucky, a few unsolicited dick pics. And by lucky, we mean we're glad you didn't have to see them until now (sorry?).