What happens after an iOS magazine subscription is canceled?
From a technical perspective your subscription is only valid as long as you're paying for it. After that Apple's servers return the same response for you, as they would if you had never subscribed. 

You will probably still keep access to all your issues, although restoring old issues has to be implemented by the app itself. For example wired magazine requires you to create a wired account to later restore all magazines. (But even without the account you can keep your downloaded issues as long as you want. I expect that to be standard across other magazines as well - but again, that's up to the publisher.)