When you leave Stony Brook, any sites you created will be removed when your account is disabled. In order to preserve your site, you can move it off Stony Brook's Google Sites to Sites through a personal Gmail account, for example. Please note that these instructions are only applicable for an original "Classic" Google site.  To move a New Google Site, you can find your site files inside your Drive, right click on the "file" to share it with a gmail acount.  Then you can open it in that gmail account, make a copy so that the gmail account is now owner of the content. 

Moving a Stony Brook Google Site 

To achieve this, share the site with your gmail account email address (at owner access level), and then once in your personal gmail, access the site and copy it.  To learn more, watch this video.