The Answer There are many places in the world today which cause this. It turns out that the burial isn't instantaneous.
Organic matter rains down to the bottom of bodies of water.
Organic matter rots, a process which consumes oxygen. And it is eaten by creatures, who of course consume oxygen. If there is any water flow into the lower region, then the oxygen level down there should be enough to sustain some lifeforms. However, in still water, the deeps only get oxygen by diffusion from the upper layers. Diffusion is slow, and rot consumes the oxygen faster than it can arrive.