This has been the case in Japan for nearly two decades by now. Deflation there started in the early 1990s, and despite the efforts by the Bank of Japan and the government through the reduction of interest rates and quantitative easing (money printing), it nevertheless persisted...
As I said, for some people it is inflation, for some others it is deflation, depends on where you are in the central bank's food chain. In an expansionary monetary policy, those who first get central bank money will always get rich regardless of inflation/deflation. And these rich guys might not be interested in spending money to stimulate the economy (which is the most inefficient use of money during a recession), they just send their money oversea and hunt for other assets
Inflation (and deflation, for that matter) is not defined on a personal basis, as you might have known. It is a general price increase or decline. Furthermore, whether or not the rich guys might be interested in spending money to stimulate the economy is not directly relevant to the point you first made, that deflation cannot exist in an expansionary monetary environment (actually, it works against your point). In fact, an expansionary monetary policy is used to fight deflation, but its mileage, as it were, may vary, and they have to coexist, at least for some time (by definition)...
The whole picture is more complex than some single formula. After 2008, added money supply just flew out and pumped up the commodity and oil price around the world, and to china, to raise the housing price in china. So the inflation can be exported, no current economy theory discuss this in detail. Even in home country, new money are mostly used to buy more and more bond, thus drive the bond inflation, but bond is not included in the CPI/PCE, the whole nation would still be dragged into deflation (Due to more debt, and less consumption as a result)
Of course those money will eventually "trickle down", but since majority of those money flowed to some other area, the effect of an expansionary monetary policy might not be felt in 5-10 years, makes the operation itself very inefficient and a waste of resource, the only thing it achieves is moving wealth to the money creator and their friends