UPDATE ON THE PROBLEM:
The solution will be let users go to /folder path for the duration of session expire time. On this path make php script for copying ALL COOKIES from /folder to / path by using setcookie function (http://php.net/manual/ro/function.setcookie.php)
foreach ($_COOKIE as $key => $value) {
setcookie($key, $value, $expire, "/")
}
// redirect to "/" now. User will be able to login.
Additional explanation: cookies are tied to path and domain, its important (and by default its /, but it seems not in your case). So PHPSESSID from subpath (like /folder or /me) not accessible from parent. And they propagate from parent to child. So cookies from /me are the same as for / with there not assigned explicit.