No, there isn't.

I get what you're asking. Maybe there's a secret website listing places that are too lazy to put up listings on the apartment listing websites. However, if there were such a place, it would just be another one of those apartment listing websites.

Like, Craigslist is a website that connects apartment buildings that don't post on MLS - but it's well-known enough that it's just part of your "places I already know about."

There are other websites like Zillow and ApartmentList, but I don't think you're just looking for another version of MLS/Apartments.com/CL. I think you're hoping for a magic list of "buildings that never list their apartments and probably have great vacancies I could get." If such a website existed, we'd all use it and then it wouldn't be the site you're looking for.