Abrindo e fechando o Chrome deve sempre excluir todos os cookies da sessão. Se isso não acontecer, há um bug.
A user's session cookie (also known as an in-memory cookie or transient cookie) for a website exists in temporary memory only while the user is reading and navigating the website. When an expiry date or validity interval is not set at cookie creation time, a session cookie is created. Web browsers normally delete session cookies when the user closes the browser.
(De Wikipedia )