The value of the property on date of death is normally the basis in inherited property. If your case, the cost would be the Fair Market value at date of death, less the mortgage on the property as your adjusted cost basis.
So if I inherited my mother's home and on date of death it was $100K that is my basis (or cost).
Now if she had debt on it of for example $40K then my basis of the home is the FMV less the debt I acquired. So in my example, due the debt on it, it is $60K adjusted basis.
The links below are to a Court Case: Crane v. Commissioner where this was the outcome.
https://double-taxation.com/2012/01/30/tax-laws-most-important-cases-volume-1-the-lasting-impression...
https://en.wikipedia.org/wiki/Crane_v._Commissioner
