If property is given during a donor’s lifetime, the donee (gift recipient) keeps the same basis as the donor for gain property. (IRC Sec. 1015(a)) For loss property, the donee’s basis is the fair market value (IRC Sec. 1015(a)), which prevents the donee receiving tax benefits from the economic losses which occurred while the donor owned the property. Basis is also increased by the amount of gift tax paid, if any. (IRC Sec. 1015(c))

See the guide "Basis"