@nomi subject/object pronouns, not subject/possessive. Feminine singular third person just happens to use "her" for both. So full sets would be
I/me/myself/my/mine
Thou/thee/thyself/thy/thine
She/her/herself/her/hers
He/him/himself/his/his
It/it/itself/its/its
We/us/ourselves/our/ours
You/you/yourselves/your/yours
They/them/themselves/their/theirs
but conventionally we just shorten it the first pair.

I'd like to see the second person singular come back!