What would happend in distant future if we didn't extract fossil fuels
Obviously if all fossil fuels had been left in the Earth it would greatly lessen the climate warming problem. You ask what would happen to these fossil fuels in the course of time if we left them alone. The coal would remain inert and fairly well behaved; some would be exposed by erosion, but would do no harm. Some would be buried even deeper as new deposits of sediment were laid on top of them.

Most of the oil would remain buried out of harm's way, but some would be exposed by erosion and geological faults to form tar pits or asphalt lakes (which are both much the same thing). Oil seepages are a nuisance, because they pollute the sea and fresh water on land. Fortunately they do not occur very often. On land, the volatile fraction evaporates quickly and leaves a thick, sticky residue called tar or asphalt, the latter being slightly thicker.

Well known examples are the La Brea tar pits in Los Angeles, famous for the fossils of extinct animals trapped by the tar, and the asphalt lake in Trinidad which has long been mined for surfacing roads etc. There are several other tar pits in California, and a large asphalt lake in Venezuela.

Looking into the future, a few more oil reservoirs would be caused to leak in the course of time by geological faults, but most would stay safely in the ground. Meanwhile the old processes would be at work, transforming vegetable matter into peat, peat and wood into lignite, and lignite into coal. Plankton and vegetable matter in the ocean would form more oil reservoirs. 

Present fossil fuel deposits will become buried more and more deeply in the course of millions of years, when man has vanished from the scene, with new layers of sediment and new fossil fuels laid down on top of them, but they will never be buried deep enough to reach the asthenosphere, never mind the centre of the Earth. They will just, in some cases, have another kilometre or two of rock placed on top of them.