@hotelbravo777 in fact if your parents were to close their account, then your mailbox and all of the mail within it is supposed to be deleted after 90 days. Now it appears that often this doesn't happen and the mailbox lingers on, only to be unceremoniously deleted years later much to the surprise of all and sundry.
So, basically, don't chance it!
Create a new email address for yourself, ideally not tied to a particular ISP, change your address on as many sites as you can and copy mail from your old mailbox to the new one - you can forward individual mail items if you want.