In Exchange 2013 you can sometimes see the following event log error (MSExchange Store Driver Submission, ID 1012):
The store driver failed to submit event <id> mailbox <guid> MDB <database guid> and couldn’t generate an NDR due to exception Microsoft.Exchange.MailboxTransport.StoreDriverCommon.InvalidSenderException
at Microsoft.Exchange.MailboxTransport.Shared.SubmissionItem.SubmissionItemUtils.CopySenderTo(SubmissionItemBase submissionItem, TransportMailItem message)
at Microsoft.Exchange.MailboxTransport.StoreDriverCommon.StorageExceptionHandler.RunUnderTableBasedExceptionHandler(IMessageConverter converter, StoreDriverDelegate workerFunction).
And this will be preceded by the following event log warning (MSexchangeIS, ID 1077):
The mailbox <guid> on database <database guid> is approaching its storage limit. A notification has been sent to the user. This warning will not be sent again for at least twenty four hours.
The mailbox in both errors is the same and it occurs for mailboxes that have moved to Exchange Server 2013 from Exchange Server 2010 and are close to their mailbox quota. To fix the issue move the mailbox to a different database. The easiest way to do this is New-MoveRequest <guid> where the same GUID is used.
If you have lots of these then this is a little more time consuming, unless you get PowerShell to the rescue.
The following two cmdlets will query the last seven days of the event logs for MSexchangeIS sourced events with ID 1077, get the event log message (which contains the mailbox guid), manipulate the string containing the message and generate a text file of just the mailbox guids. The second cmdlet will run a New-MoveRequest for each mailbox listed in the text file.
Make sure though that your Application event log is large enough to store more than seven days of events and then run these cmdlets, per server every seven days until the issue goes away (or over the course of say a year, move all mailboxes to different databases and that fixes it as well).