The theory of Higurashi When They Cry Meguri is thus:
Rika is an Oni and the Rika we see is infact Bernkastel the Witch that Rika uses to entertain herself until her boredom drives her outside to the public where she risks death or being shoved into a laboratory. There may be a happy ending for her considering Higurashi When They Cry Mei’s story but the damage of isolating herself for centuries will be done.
Umineko When They Cry and Ciconia When They Cry are all metaphors for Rika’s frightening condition.
There isn’t 19, 18 or even 17 People on the island: There is only 1 person on the island and that is Rika a scared girl with horns who lived for centuries alone afraid of being killed out of fear for her horns.
Edit: Changed title because I’m quite certain that I accidentally posted further theories past this post.