Hey there @victorlacombe !
Yup, this should be possible to do. Super Users can’t do this as it requires at least a moderator. But you should be able to change the status fairly easily. You might need to head into Control though, as I don’t think the option will show up on the front end.
If the status is removed, the question is re-opened and unset. However, if you change the best answer instead, the thread will simply be updated to show the new one. Any points awarded will be recalculated and this may affect roles/ranks that rely on best answers.
Alternatively, one possible “hack” would be to convert the thread to a Conversation and then back to a Question. This should clear the status and reset it.