First of all, fosils are most broadly defined as remnant, impression, or trace of an organism of past geologic ages that has been preserved in the Earth's crust.
Fossil do not need to be mineralized to be fossils. From what I have observed about fossils from the North sea when caught in fish trawlers net, there is little mineralization up to 30-40,000 years. However, Eemian (Sangamonian) remains >130,000 years are heavily mineralized.
The setback here is that those fossils can not be dated radiological because of that chemical alteration. So we assume something to be "Eemian" or "Sangamonian" from other clues. I've seen an "Eemian" vertebra of a Arctic whale that was not mineralized at all, the complete skeleton was found on a hill (!) at one of the October revolution Islands, north of Siberia.