You will receive a Quota Exceeded bounceback message when you attempt to email someone that has a full mailbox. Until the user makes space in their mailbox, or the quota has been increased, you will be unable to send them any messages. Below is what a version of the bounceback could look like.
This message was created automatically by mail delivery software.
A message that you sent could not be delivered to one or more of its recipients. This is a permanent error.
The following address(es) failed:
test@site5demo.com
SMTP error from remote mail server after RCPT TO:<test@test.com>:
host site5demo.com [174.120.241.66]: 550 Mailbox quota exceeded
With some providers, you will have to click the on an attachment to read the error.
If all the email accounts are receiving a quota exceeded message,
your actual hosting account could be at its quota limit. If this is the
case, you can try deleting unused emails from your account to see if
that resolves the issue.