single word requests - Is there a term that describes leaving out the implied subject of a question?

For example, "Not going? Be sure to cancel at least 24 hours in advance." has an implied "Are you…" in front. Is there a term for this concept?

Is it proper grammar (or at least accepted in business communication)? I feel I've seen this structure use a lot.

Update

Is this just an example of conversational deletion? I'm guessing "conversational" means it would be generally okay for marketing and user interfaces but not for a memo to the CEO (or other more formal documents).