When property is gifted to you, the Net Operating Loss (NOL) carryover from your parents' tax return does not transfer to you. NOLs are personal to the taxpayer who incurred them and cannot be transferred with the property.
Regarding the basis of the property:
- If the Fair Market Value (FMV) at the time of the gift is equal to or greater than the donor's adjusted basis: Your basis is the donor's adjusted basis just before the gift, adjusted for any changes while you hold the property.
- If the donor paid gift tax on the gift after 1976: Increase your basis by the gift tax paid on the net increase in value.
For more details, refer IRS article on Basis of Assets.