Backlinks are of two kinds once they are external.
The one linking to your main domain's URL and should be the majority, and the deep backlinks, the ones that link to a pages inside your site, within a sub folder or just a page not being the home page.
The Deep backlinks are very important now days, because, Search Engines will measure the ratio between the Home page Backlinks and the Deep ones.
Having a good proportion of deep links means people find interesting content in it and are sharing with others, they look more natural that a home page one, you follow the idea ?
To answer then, the link you are talking about are deep backlinks and thus very important.
Now, if a page is no more on line, I am not this sure, only thing I am sure of, is HTTP 301 is the safest, because I don't think deep 404 (or "page not exist") linking is that good or even taken into account.
But the links exists and mention you domain, so, bots see it.
With an HTTP 301 making sure no, old deleted page are 404, but are redirected to either the new URL of this particular page or to home when there are many is perfect.
This way for sure backlinks won't be lost and PageRank Transmitted.