The answer here depends on how the website handles cookie management. If they're doing things correctly, following the signout link should invalidate the cookie on the server-side and also remove it from the client.
As such if an attacker got access to your PC after that they shouldn't be able to mis-use the cookie, even if they could get access to it.
If you're still logged in and leave your PC, without shutting the browser, it's likely that an attacker could grab the cookie just by using the browser. If they only have access to your hard drive (eg, over a network), they may be able to get access to the cookie file, but it could be somewhat more tricky to exploit.
two-factor authentication may help in the scenario where someone steals a cookie while you're logged in, but while the session is ongoing it's likely there will be cookies on the machine which will provide access.
The safest bet is to ensure that you log out of all sessions before leaving your computer and also close the browser (a lot of session cookies are removed from the client when the browser is closed)