Mailbox Size Limit - Disruption of Service - Warnings etc...

If we set a mailbox size limit for an account and that account reaches that limit.... are all new emails rejected and a notice sent to the sender? Will the server hold onto the emails for a particular amount of time giving the user/account time to increase their limit or free up storage and then deliver the emails? What happens exactly? Also, does cPanel send out a notice/warning when the customers is close to reaching their storage limit? Thank you.