saved in the browser
This is pretty much just best practice. When's the last time you could change your password without entering the original, short of a re-verification via email? Same idea here.
which, if the persons password is saved in their browser, would pass through to the website, granting a re-auth.
I got you now. I've been using 3rd party password managers (with a timeout for a forced reauth) long enough that I forgot when you let the browser do it it's not nearly so locked down.