I decided to remove bunch of thin pages few months ago (they are 404 now). I discovered recently that lot of them have quite a lot of backlinks. Now the question is : Is link juice still passed from those backlinks to domain or should I change 404 to e.g. 301 and pass link juice to e.g. index.html ?
In my opinion you should take a close look at these backlinks before you decide anything. There are often many fake referral links that appear in your logs but don't actually exist. If you have a lot of these, plus a lot of worthless spammy links, and you don't get any traffic from any of them, these are the types of links that can do more harm than good. Maybe the best thing to do is to just ignore them, or else disavow them..
In SEO the word "natural" usually refers to backlinks that another person (a real human being) voluntarily gives you because they think your site has valuable information or resources that would interest their visitors. This type of backlink can be identified by looking at the legitimacy of the other website and the context in which the link appears. These are "real" natural backlinks. The best ones will send you real traffic.
Auto-generated spammy backlinks generally don't come from reputable websites, normally don't send any traffic, and in most cases don't provide any significant pagerank. They should not be counted as "real" natural backlinks.
Not to mention that returning a completely different page for a page that no longer exists or has any content from the 404 page is called a soft 404 and is not a good thing, ever. IF the thin pages' content is now on a different page the request should have had a 301 redirect to the page where the content now resides. If it does not exist anywhere, leave it as a 404.
To help you check the value of backlinks, Webmaster World offers some Free Tools to check backlinks: [freetools.webmasterworld.com...] - there is a link to the Free Tools at the top of the page.