PSA: Chrome and Firefox do not always clear session cookies on exit
Cookies without an expiration timestamp are called "session cookies".  They should only be kept until the end of the browsing session.
However, when Chrome or Firefox are configured to reopen tabs from last time upon start, they will keep session cookies when closing the browser. This even applies to tabs that were closed before shutting down the browser.
 We are not talking about the the Rails
session cookie here, though it often is a session cookie.