If your application relies on the creator’s Twitter Username, you got the whole oAuth concept wrong and probably have some very bad security issue in your App.
An Application has two different ways of Authentication:
- App Auth: Using a bearer token, used if the App needs read-only access to public data and not be tied to a special Account
- User Auth: Log-in an user using oAuth and get credentials for it, needed when the App needs to to things in behalf of the User
So, in case 1. the App should still have access to the Tweets of User X even if User X has blocked the creator of the App. In case 2. the User using the App would have no longer access to the Tweets of User X, if she has blocked the authenticated User. (The App creator doesn’t matter regardless of the case)