UPDATE ON THE PROBLEM:
If you send manually the header with new expiring date for desired path, the client should remove it.
session_start();
header("Set-Cookie:PHPSESSID=".session_id()."; expires=Sat, 07-Nov-1999 14:58:07 GMT; path=/cv/");
The first time, you have the old cookie path, but from the second page call only the cookie in path / will be stored and transmitted.
You can send this header when you know if the client is affected by this problem or having this for some month.