session_destroy() but re-use session ID: security risk?

Say an application, using sessions, has a "logout" button which destroys the session data. Say, also, that a user clicks that button, but then logs back into the site without first closing their browser. Under these circumstances, the session cookie and ID from their previous session will get re-used for their new session. Is there any harm in this, from a security viewpoint, or otherwise? TIA Kirk