if SSL certificate expires. the user should get a pop-up in any browser, denoting SSL certificate issues. and noting something about it has expired.
it has been some time since i had to deal with SSL certificates. so i am out of loop of current standards for them. at one time you needed a min of 2 computers. and hacks for single computer were hard to come by. 1 computer that issued certificate and 2nd computer (your site) that obtained the certificate. thinking about it. there is some DNS records that get created to deal with SSL.
SSL certificates are designed to expire after so long. (security reasons) there are some applications i would imagine to do a test bed server to create certificate, without having to pay for a SSL certificate.
back in the day there were so many settings and options for SSL it got a little overboard. not sure how it is today.