Well, my understanding is that each new page has an initial PR assigned to. (This initial PR assigned is higher for videos.) That's the secret behind blog networks and why Google hates them so much. Basically a blog in a blog network is getting high PR automatically simply by posting other people's content. With a good inter-linking structure, when the number of pages increase, PR adds up and the PR of the website increases even without backlinks. It simply means the initial PR of the pages affect each other and as a result the PR for the whole website goes up. (The best example for this is Tumblr as a whole)
Now, my question is: let's say you get one of these high PR blogs all with crap content (similar to ALN posts) and no backlinks (BTW, it is not the property that I am talking about but it is good for the sake of example). It currently has a high PR and hundreds or thousands of crappy content pages, but there are chances that Google eventually penalized and de-indexes the blog. There are two ways in my opinion to keep that PR:
1- Remove all the crap content and post good content (which I am wondering if that would work, because the source of PR (internal pages) will be gone.)
2- Use this website as a source of backlink to other websites either with a blogroll or with posts linking to the other websites. I know that this one would work, but eventually the target websites will be at some risk too, although not as great as the main high PR blog.
So the question is how to keep the PR that has been accumulated and transform it with better content to some quality content websites...

Just because the backlink checker you are using doesn't show any, doesn't mean they don't have backlinks. Most backlink checkers are unreliable. They usually do not pick up internal links either. All the links might be internal links.