I wonder what they're going to do when the promotion time runs out. If they're going to delete or block access to a random 3 GB of data in someone's dropbox, they're going to be dealing with a lot of upset customers.
(Should these people be aware of the fact that their space is going to run out, and have up-to-date backups of their stuff? Obviously. But the hard fact of life is that people do use dropbox as their only backup, and if something goes wrong there, they're going to be a customer support headache.)
The way it currently works is that they just don't allow you to upload anything until you're below your limit. They continue to store whatever is there, and do not delete it.
(Should these people be aware of the fact that their space is going to run out, and have up-to-date backups of their stuff? Obviously. But the hard fact of life is that people do use dropbox as their only backup, and if something goes wrong there, they're going to be a customer support headache.)