To predecease someone is to die before they do. If, tragically, your goldfish dies one week and your gerbil passes away the following week, you can say the fish predeceases the gerbil.
While you can use this verb to talk about any person or animal's death — or even the death of your favorite houseplants — it's most common to describe one family member predeceasing another. It's devastating when a child predeceases his or her parents, or when one twin predeceases the other. This sixteenth century word uses the "before" prefix pre- and decease, from the Latin decessus, or "death."