There a few options for users with Gmail Storage reaching capacity; 

  1. Delete old messages with attachment - (screenshot)
  2. Create a new "jon.archive@domain.com", then migrate the oldest mail to jon.archive@domain.com.  After the migration, delegate access of "jon.archive@domain.com" to "jon@domain.com".  That makes it fairly straight forward for them to access their historical mail.  You can also set the default send as in the "jon.archive@domain.com" account to be "jon@domain.com" .  That way if they do need to reply to any historical mail they could do so.           *for additional information on the migration process email support@ditoweb.com