First, "своё would be the "neuter person". And second, the Russian pronoun “Свой” means “one’s own”. It replaces the normal possessive pronoun when it refers to the subject. Example “Ivan loves his (own) dog (Иван любит свою собаку)”. If you were to use the normal possessive pronoun it would indicate the dog belongs to someone else.
It's just a little joke indicating that in some cases the dots above 'ё' do matter. "Princesses who were confined by a dragon can be saved (there is a possibility to save them), but those who were sharpened by a dragon... Sorry".
ЗаточЁнных comes from the word заточать = to confine, imprison (this word hardly ever used nowadays)
ЗатОченных comes from the word затачивать = to sharpen (like, to sharpen a pencil)