Do cookies expire on the server side or on the client/browser side?

I know that if i login to a website, i get set-cookie headers with max-age/expires values, that tell when these cookies expire. Now what i want to know is, do these cookies expire on the client side? so the browser gets rid of them, OR on the server side so the server blocks/deletes them? i'm asking to see if it is possible for someone to extend the age of cookies using something like fiddler/charlesProxy.