You can download resources that are marked as "Rejected until Updated", but they don't show up in the resource database pages (you can't even use the built-in search to find it). You can only find them by searching for threads started by the authors (easiest way is to enter the author's profile page, click on the "Statistic" tab and choose "Find all threads started by *user*").
Note that these models can have technical and/or cosmetic flaws, so it's not guaranteed that they will work properly.
If you can't see and/or download a resource at all (but still can see the comments), then that resource is marked as "Permanently rejected". And there are many valid reasons why these kinds of models are marked that way.