It works in some cases.

• For commodities with 'elastic demand', a lower price will increase demand (at least up to some limit of satiation). For example, say, luxury cars. Lots of people would like to drive a luxury car instead of a regular one, and if luxury cars became very cheap, more people would upgrade to one, thus increasing demand. But it doesn't hold true for inelastic demand. If cars in general became very cheap, it would only increase demand up to a point ... then, once everyone who wants a car already has one (or several), there's not much reason for anyone to buy even more.

• For commodities with demand currently suppressed by high price. Healthcare is a good example of something with (mostly) inelastic demand. The amount of healthcare people need doesn't really change depending on the price, and (most) people have no motivation to go out and get more healthcare than they actually need. But in the US, healthcare is very expensive, with many people not getting as much as they need because of how expensive it is, which has reduced demand below the level it 'should' be at. If healthcare became cheap, demand would increase back to the 'normal' level, then stay there.