DNA replicates itself, so no, unlike what it may seem, parent organisms do not loose their DNA. Before the fecundation process, a cool process similar to miosis happens, it is called meiosis. During meiosis the parent chromosome will duplicate it self and break down each of its 46 chromosomes into 4 different new formed cells, which will become the sperm and egg cells. Each of these egg or sperm cells will be different from eachother, which is how you get siblings that don't look alike, however they will contain a copy of the parent's genetic information.
In conclusion;
In the creation of offspring, the copy of the parent's DNA breaks apart into 4 different pieces which will form sperm or egg cells.
