If they are creating / managing a document: let them know what is happening and allow only local saves until resolved or a specific amount of free space opens; you can take an existing cloud-based document and move it to a cache so to prevent data loss or just store it locally. UIDocument and its lifecycle is pretty rich with error handling so there's a lot of opportunity to handle this situation.
If you are using CloudKit, there are different options based on what you are doing and what you mean. If the user has run out of space, you should tell them and then either cache changes locally (to push up when done), treat the situation as if the user has logged out, or just prevent edits if there's no local store mechanism in place.
There is no way to donate data to the user, this is a situation in which they need to resolve and the good news is that the system will be prompting them all over outside of our app. Ideally, you'd let them know once per session, what the app is doing until that problem is resolved, and continue to let their interaction move forward.