"Remember me" would be a good function but at this day and age usually chrome saves your username and password as well so when I get logged out my credientials are usually already there thanks to chrome saving that and allowing me to just simply click log in.
This is a bit off topic but I am not sure if you are just giving an example of how it looks when a browser saves your passwords or if you are using this feature yourself!? If you are, you should seriously reconsider saving your passwords with Chrome or other browsers. Especially passwords related to your financials or private info. It is not that hard to extract the data.
https://hackernoon.com/why-you-should-never-save-passwords-on-chrome-or-firefox-96b770cfd0d0