If your mother continued to live in the house after she transferred it to her children, the IRS deems the property to be in her taxable estate even though she gave it away before her death. This is irrelevant for estate tax purposes since only estates over $11.2 million are taxable, but it’s good for capital gains purposes. As a result of being in your mother’s estate, the basis for the house was changed on her death to its fair market value on that date. This is often called a “step-up” in basis. As a result, the only gain that is taxed to the children is the difference between the fair market value when she died and the net proceeds of the sale, which is probably zero, resulting in no tax.
For more information on paying capital gains on property you inherit, click here.