It might be odd to think of DNA having a half-life, as it’s usually associated with radioactive material — but as it measures the time taken for half of something to decay, it makes sense to talk about old samples of DNA in the same way. For example, uranium-235, the fissile material that can be used in nuclear power plants (and nuclear weapons), has a half-life of 703.8 million years. DNA, by comparison, doesn’t fare so well — according to a study of 158 samples of moa bones between 500 and 6,000 years old, DNA appears to have a half-life of around 521 years.
Actually, anything driven by a simple probability is going to behave this way, where the rate of loss depends on how much you have. There are biological half-lives for some substances you ingest, which tells you how long it will take to metabolize or excrete that substance.