I believe the process of fossilization still occurs today. The reason being why we find fossils is because of the overlaying of earth's substances over the fossil, and with the right combination, lead to fossils. It would still occur today, let's say you've buried a dog, and over time water, smelted rock, and a few other earth materials came over the dead dog's body. It would most likely be fossilized at the end of this process, but it would take years for it to happen. Fossilization does not happen in one day.
