Is it possible to close out an email account?

Yes it is. Go here: https://edit.yahoo.com/config/delete_user

Follow all the prompts when you close out your account. Please be sure to read all warnings very carefully during the account deletion process.

Warning: once you terminated your account, you will lose access to it as well as all of your stored information.

I think it depends on the email provider. Most of the times this is impossible to be done instantly. You have to avoid opening your email account for a large period of time (i.e. 2 months or more). Then your account will be deactivated, all your incoming and outgoing emails will have been erased and you will be able to re-open it with a few clicks. After a larger period of time (i.e. 1 or 2 years). Your account will close permanently. Just check out your email provider's terms of service and you'll find out for sure!