When cells die, whether through apoptosis or necrosis, the DNA and other molecules found in those cells don't just disappear. They wind up in the blood stream, where degraded bits and pieces can be extracted.
This cell-free DNA (cfDNA) is degraded due to its exposure to enzymes in the blood but is nonetheless a powerful monitoring tool in cancer, pregnancy and organ transplantation. One fairly recent breakthrough is prenatal testing for conditions such as Down syndrome, as fragments of fetal cfDNA can be detected in a mother's bloodstream.