If, however, you wait and bequeath the stock to them at your death, the shares would get a new tax basis at that point. If the stock is worth more than what you paid, your kids get that new, higher basis. So if it’s worth $25 on the day you die and they sell for $25, no capital gains taxes are owed. If it’s worth $5 when you die, though, the capital loss essentially evaporates. Your kids can’t use it to offset other income.