When a mailbox exceeds its storage quota, new mail delivery or mailbox performance can be affected depending on how the platform is configured. Existing mail usually remains, but users may stop receiving new messages until space is freed or the mailbox allocation is increased.
The fastest ways to recover are to delete unnecessary mail, empty trash or spam folders if they count toward usage, archive old messages elsewhere, or upgrade the storage allocation if your plan supports it.
If mail appears to be missing, always check quota usage before assuming there is a delivery issue.