Small bits of DNA information can be found in ancient remains. In analogy to old bones becoming mineralized, is there a chemical environment in which the nucleic acid sequence of the original strand might remain readable though in other, more stable, chemical form?
A mineralized form might be possible (maybe DNA can form a pattern of missing atoms in stone) but reading it will be next to impossible. We have many techniques to amplify and read tiny bits of DNA, doing this for imprints in stone would be a huge challenge, especially because many (all?) techniques for reading DNA depend on the amplification of DNA.
As for conservation, as far as I know most of the damage making the DNA unreadable is hydrolysis of the backbone. If the DNA is in an environment without water this will not happen. Of course you need an extremely dry environment for DNA to last millions of years.