I have seen pages stay in the SERPS despite all links being removed
Yes spiders may keep accessing them no matter what you do. If the links are listed on other domains bots will follow. So for example if you buy a domain and post completely different content the spiders may keep accessing the old links for an eternity no matter what headers you output 200, 301, 404 doesn't matter. They will follow any url if they find it internal or external.
Now if you see errors in GWT it maybe different and signify a problem with the application somehow generating invalid urls. You need to watch for those and in many cases google doesn't even state the path to trace them.