For example, if you access this url :http://stackoverflow.com/questions/286004/hidden-features-of-modrewrite and this one http://stackoverflow.com/questions/286004/hidden-features-of-modrewrite-PUT_ANYTHING_YOU_WANT_HERE. It goes right to the same page, and it seems Stackoverflow doesn't check for a valid slug (as wordpress calls it).
http://stackoverflow.com/questions/1932501/better-use-only-id +)
String is only for user-friendlieness.
I don't see any reason to check the slug if you already have the id. Users shouldn't manually change the URL's, but no harm is done if they do.
Some web applications only have a slug (no id), but then extra care has to be taken to ensure it is unique. Just including and checking the id is much simpler, especially in frameworks like rails.
I'd use just the ID as the slug may change but you'd still want old links to work.
For example, if someone edited the title of their question you'd want to change the slug appropriately, but you wouldn't want old links to the question to stop working.
Since the numerical ID is the only information needed to identify the resource, the slug has only descriptive characteristics. But this description should be appropriate to the resource. So, yes, you should check if the slug is the proper one and correct it if not.