Let me reply to your statements in two parts.

“If there is simply emptiness, or nothingness, after physical death, what is it that becomes of us?”

At death, the sense of being a separate individual will clearly end (even in a more profound way for someone who has died to “his” or “her” individuality during this lifetime). Not any thing, then, will become anything. In other words, the nothingness which has always been, as the ultimate condition, will merely, continue to be–as has always been.  

“You” do not even become this. There is only this.

Lastly, in the teaching of advaita, we speak of the relative and the Absolute, primarily as teaching tools. A person can ask questions about the Absolute, and can receive answers.

Once advaita is understood, its intention is to point our attention to ajata vada, the final teaching of emptiness, or nothingness. Nothing MEANS nothing. There are no questions we can ask, and expect any answers, concerning NOTHING. It has no qualities, quantities, attributes.

As long as we speak, in nonduality, of the relative and the Absolute–even to acknowledge that these two are One–there is still a subtle duality. And so the duality of “question” and “answer” remains applicable. But when the question concerns nothingness, or emptiness, silence would be the only legitimate reply.