Trees are part of a closed cycle: eventually they burn or are decomposed biologically (fungi and animals). As far as I know, all the high quality fossil reservoirs we excavate have been accumulated in an exceptional era when the biological defense mechanisms of trees happened to have so much of an upper hand over all potential decompositors that their corpses basically stayed around forever. Imagine a C heap when for a while free() is a noop... (it has been fixed for quite a while now).

The closest thing we have today to those "eternal tree corpses" are peat bogs were decomposition is kind of broken even today (and guess who discovered that dried up peat can burn, even if it's a very dirty fire? Humans. We just love oxydating carbons).

I think they mean 'after the tree has been cut down or otherwise reached the end of its life'.