I believe the sender would've received an error code / mail delivery failure message when the quota of the receiver was exceeded.
Exchange mailbox
- Exchange mailboxes have two quotas, a soft lower quota and an hard upper quota.
- Users with mailboxes approaching the lower quota limit will receive warning notification via email.
- Some mail programs display a quota warning message onscreen, but others do not and rely on your noticing the email reminder.
- An account that exceeds the lower quota limit will not be able to send mail (but see Commentary).
- Attempts to send mail will show an error message. Incoming mail can still be received, as long as the account has not yet exceeded the upper quota limit.
- You must delete items to get below the quota limit to be able to resume sending mail. - Note that messages in your Deleted Items folder still count against your quota. You must get them out of your Deleted Items folder, by shift-deleting individual items or by emptying the whole Deleted Items folder.
- An account that exceeds the upper quota limit will be blocked from receiving mail and from storing new messages. Your account will not be able to send mail and will not be able to receive mail.
- New mail addressed to an account that is over the upper quota may be immediately returned to the sender with an error message, without being stored for delivery attempts.
http://kb.mit.edu/confluence/display/istcontrib/What+happens+when+a+mailbox+goes+over+quota