Hi Kurt,
If the will makes a gift to a person who dies within 30 days after the will-maker’s death, the will is to take effect as if the person died immediately before the will-maker. Therefore, the gift will go into the residuary of the estate or otherwise treated as if the gift was not included in the will. However you can state in your will that this is not the case, so check the will first.
If the person died after 30 days after the testator's death, then their inheritance will go to their estate.