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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).

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    A very common expression can't be said to be ungrammatical. Of course you could say it is informal, or inappropriate in formal writing. – MetaEd Jun 23 '16 at 20:27
  • @MετάEd Good point. I edited the question to clarify the "is it proper?" question – David J Jun 23 '16 at 20:30
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    This is answered at Pronoun “you” can be omitted as subject in imperative form, what other pronouns can be omitted, when and why?, but someone will probably claim that doesn't make it a duplicate. – Edwin Ashworth Jun 23 '16 at 21:18
  • @EdwinAshworth I went ahead and flagged it, although technically I was asking what the concept is called ;-) Seems to be "Conversational Deletion", since that was mentioned in answers in both questions (the one I linked & the one you linked). Whatever helps future Internetters find the answer! – David J Jun 23 '16 at 21:28
  • A search for 'omit subject' gets you into the various duplicates. – Edwin Ashworth Jun 23 '16 at 21:35