The solution was to add `&closed=-1` to http://api.openstreetmap.org/api/0.6/notes/feed?bbox=smaller_longitude,smaller_latitude,larger_longitude,larger_latitude, like described here:
https://wiki.openstreetmap.org/wiki/API_v0.6#Map_Notes_API
The link is mentioned on https://wiki.openstreetmap.org/wiki/Notes/API_and_development (which is mentioned on https://wiki.openstreetmap.org/wiki/Notes).
https://wiki.openstreetmap.org/wiki/Notes ).
If there are other ways to display hidden notes, feel free to share.