https://www.merriam-webster.com/dictionary/themselves, see "Can they, their, them, and themselves be used as singular pronouns?"
What would be the correct pronouns here in your view?
(Edit: Actually the more I think about that the less I'm sure what I'd say..)
> or even, "Someone came into this room. I don't know them, but they took everything."
"Them" would still be plural by your earlier logic though. Unless you're suggesting that you think "themselves" is plural and "themself" would be the singular?