When I post a question and it is downvoted below 0, it would be useful to receive a notification so that I could edit the question or add a comment. An option for email alerts would be even better.
Now, when it comes to notifications, it is valid to consider whether the cost of informing the user (attention is finite) is greater than the value gained from the notification. If a post goes below 0, then that is extremely relevant information, as it usually indicates that the user has to take action ASAP to prevent the question being closed. I think it is easily valuable enough to be worth informing the user.
- Notifications on close or deletion - also a good idea