The only case I can currently think of that cannot be solved using continuation tokens sent to the client is where the order of the items that are enumerated may change between calls to the API. For example, imagine that you are fetching items sorted by score, and somebody upvotes or downvotes an item while you are enumerating them. In that case it is very difficult to encode enough information in the continuation token. (I can think of complicated ways to make it work, but the resulting database queries would be horrible.)
But for simple stuff like deleted items and similar, it is easy. If you leave out sorting it is trivial to implement as well -- all you need is to enumerate the items based on an internal ID that is guaranteed to always increase, filtering them as required. The continuation token will simply be the ID of the last item you evaluated and the filter that is applied. On the next request you just resume from that ID. If that item ID happens to be deleted in the meantime it is no problem. You just resume from the next one available. I.e.:
SELECT * FROM items WHERE id > :last_returned_id AND [insert-filter-here] ORDER BY id LIMIT 100;