I think if we take informing as a noun in this sentence, it should be fine. What are your views on the grammaticality of the following sentence?
He left me without informing.
Inform is a transitive verb; as such, it requires an object. He left without informing whom? You, or someone else? If, in fact, it was you whom he failed to inform:
Note that you can remove the first "me", not the second one.
Now, if you write it the way you wanted to write it,
and you expect the reader to take this as a noun (the gerund, "informing"), you are asking the reader to parse it like this:
So you are saying it's like :
He left me without bread.
He left me without a clue.
This means that YOU are the one lacking the item.
Now, if the item is "informing", that means the act of informing; that is, the act of telling someone something. So, leaving you without "informing" would mean that he left without giving YOU a chance to inform HIM!
Of course, this is not what you meant. Because the thing he left you without was information (the result of being informed).
But this phrasing does not clarify that it was from HIM that you expected that information. It could be just any information.
The other problem is that "informing" and "information" are not countable nouns. So we don't say one informing, two informings, and we don't say an informing or an information.
However If you were to use a countable noun (for instance, "warning"), it would sound OK to use the indefinite article "a"
This, I believe, conveys your intended meaning.
But since "warn" is also a transitive verb, you could also say.
I hope this helps you to understand the subtle difference.