Residence Permit expiration, what to do

i'm just about done with my job in here but i still want to go to visit Tibet. my residence permit is to expire soon and my employeer is not the person to trust if it comes to dealing with all those issues (i found out i'm not registered or anything so basicaly working illigally) so i prefer to do it all by myself for the peace of mind. what can i achieve? do i have to apply for a new visa, or are there any other ways? i've read somewhere (an unofficial source) that i can go to Foreign Affairs Bureau and get some time allotted (in form of 1month L type) to leave the country. is that right? and if not what are the proceedings in cases as mine?
thanks a lot for your time.