As stated already a redirect is something we can do to a web request, ie the web browser requests an url and we can redirect to a different one. With no web request there is nothing to redirect and we don't even know if the user still has his web browser open or not.
My suggestion is just configure a short session timeout and in site settings don't check the box to allow persistent login so if the session times out then the user is no longer logged in and any protected page would redirect him to login if he makes a new request.
For more info see Controlling Browser Sessions
Hope that helps,