Let me start out with an extreme (and very silly) assumption, just so I can explain something simply. Assume that the demand for currency does not depend on the price level, nor on real income, nor on interest rates, nor on anything. It's just fixed. Every individual wants to hold exactly $100 in currency, no more no less, regardless of anything.
And let's start out with a very simple monetary system. There's a central bank that issues currency, that people use as their sole medium of exchange, to buy and sell everything else. No other banks at all. So it's a simple money supply function, and a totally degenerate money demand function Md = $100 x population.
And let's start out in monetary equilibrium, where the money supply (the stock of currency in circulation) is exactly $100 per person.
Is Helicopter Money impossible? If the central bank prints more currency, and drops it out of a helicopter, will the people refuse to pick it up, and leave the newly-printed notes lying on the sidewalk?