It's still in there, but no longer directing protein synthesis.
Eventually the DNA breaks up and disappears. Even if the dead cells are quickly frozen, like those frozen dead mammoths that have been found in the Siberian arctic, the DNA quickly breaks up into lots of little fragments that make it difficult to reconstruct.
I believe that it's partly natural occurring DNAse enzymes in the cell that break up the DNA, and partly the effect of environmental conditions, particularly DNA's interactions with water. Living cells have natural DNA repair mechanisms, but these stop functioning when the cell dies, so the DNA degradation processes prevail.
This report suggests that DNA has a 'half-life' of 521 years.
http://www.nature.com/news/dna-has-a-521-year-half-life-1.11555