At https://www.sciencenews.org/article/mammoths-extinct-earlier-edna-evidence … we are told paleontologists may be led astray by ancient DNA. For example, in 2021, an analysis of plant and animal DNA in regions bordering the Arctic, spanning the last 50,000 years, suggested mammoths survived in north and central Siberia as late as around 3900 years ago, something of a surprise at the time. This was much later that the youngest mammoth fossil found in continental Eurasia. Only on Wrangel Island, off the coast of northern Siberia, and the nearby Priboloff Islands, in the Bering Sea, where they survived much longer than animals on the mainland that are, or were, thought to have disappeared not long after the end of the Ice Age – or in concert with the end of that period [or the Younger Dryas event]. The idea they may have survived until around 2000BC came about as a result of the discovery of DNA in sediments. Note – sedients rather than fossil bones. Similar genetic evidence, from the self same sediments, appeared to show that woolly rhinoceros and horses also survived long after the end of the Ice Age. One might suspect that genetics has proceeded too fast and too quickly and has come a cropper, although there is no intrinsic reason why horses, for example, could not have survived [assuming they were of a similar size o the modern varieties]. Mammoths eat a lot of vegetation, and have similar eating habits to modern elephants. They too are not that much bigger than African elephants, so the idea is not impossible.
The thrust of the article is that animal bones, especially large ones as in a mammoth thigh bone or even its teeth, weather slowly in the frigid north and can linger in the ground for hundreds of years. Thousands of years might be a bit over the top but the argument is that the DNA, and the grounded down bone [converted into a flour like texture] might well continue as a component in soils and sediments for a very long time. See https://doi.org/10.1038/s41586-022-05416-3 … but you may also like to read the original article on DNA in sediments at https://doi.org/10.1038/s41586-021-04016-x … as both sides are rather complicated in their arguments.
In the same issue of Nature journal we also have an article in support of the sediment dating original piece – see https://doi.org/10.1038/s41586-022-05417-2 … and the same story is at https://phys.org/news/2022-11-mammoth-problem-extinction-timeline.html … where human involvement in their extinction is aired. In fact, it is the underlying question as even an end of Ice Age extinction was supposed to involve human hunters. For now, everything on the subject is open to more research, so expect a flurry of support or denial of the DNA in sediments.