Please note, that it could be that this person, that you are trying to delete is attached to any other individual on your family tree.
Therefore, in order to delete such person, first - try to detach this person from other individuals on your family tree, by going to this person's card > click "add" on the left corner of the card > remove connection > choose to detach this person from his family > then please try to delete this person once again.
It seems, that I was always working in the Classic mode, and there is no Options in the Classic mode. And when I delete a person in the Classic mode it becomes unknown, and there are no buttons to get rid of relations.
Only when I switched to Modern tree mode, I noticed the Options button, and inside I found all what you're saying, and yes, I managed to successfully delete persons completely.