In my informal, colloquial understanding, the thinking behind your assertion is that during a downturn, the populous has less money to spend, thus, less product is sold. In order to attempt to sell product, vendors reduce prices as much as they can. This is classic supply and demand, where the supply exceeds demand.
Inflation is only really measured by some people wandering around stores making notes of the prices being asked for a range of products (yeah, it's a little more complicated than that, but you get the idea). If those prices get collectively discounted enough then you have deflation. The "basket" of goods that are price checked are usually picked to be broad across the economy, yet be things that "most people buy".
The basket method of inflation/deflation measurement means that for deflation to become truly likely, then the downturn needs to affect pretty much all sectors of the economy - and actually, analysis of most downturns shows that some sectors are hit harder than others. As a result, official deflation doesn't actually happen nearly as often as the simple assertion you make would suggest - even though vast swathes of people may be close to destitution, others may be working in fairly stable circumstances.
By way of example, during Covid lockdowns, many people have found themselves without work to do (leaving some unpaid or on government support), yet others have been employed as normal, or possibly be even busier than normal. Thus, whatever longer term downturns may occur as a result of it, we may not see official deflation because some sectors of the economy are (for the time being) still working roughly normally. The fact that many people have dramatically less disposable income, and so are consuming dramatically less is somewhat hidden by a single number describing the state of the economy (ie. the inflation figure) - arguably a case of over-simplification of a complex system.