What does the presence of fossils of an organism in the deeper layers of the Earth predict?

Fossils are the physical remains of extinct plants and animals or their imprints preserved in rocks and layers of Earth. They are the direct proof of evolution. 

The fossilized remnants of recently extinct plants and animals are discovered close to the Earth's surface, while the older fossils are buried deeper inside the layers of the Earth and need proper tools and techniques to discover them.