When you inherit property, the tax basis is the fair market value on the date of death of the person who bequeathed it to you. If the person had bought the stock for $50 per share and it was only $10 per share on his date of death, the "stepped down" basis would be $10; you cannot take advantage of the unrealized $40 per share loss. At the same time, had the asset appreciated from $50 to $75 per share, then you would not have to pay income taxes on the deceased's unrealized $25 per share gain. Once you sell the shares, you will have a capital gain or loss and your basis will be the fair market value of the stock as of the date of the decendent’s death.
There may be some circumstances where it would be wiser for any worthless stock to be sold prior to a decedent’s death, if the decendent is able to take any advantage from the loss on the sale of the stock.
Example: John is 85 and in good health. He has a stock portfolio of $500,000 which is handled by a broker. He also holds a large amount of worthless stock in ABC company, that is not handled by the broker. John has been holding on to that stock in the hopes that it would some day rally. John has been paying tax on fairly significant amounts of capital gains tax from stock transactions in the rest of his portfolio. The worthless stock will provide virtually no benefit to his son, Michael when Michael inherits the stock. Michael will get a stepped-up basis on the stock that is performing well. It would be wiser for John to offset his current capital gains by disposing of the worthless stock, rather than hoping that it would eventually rally and perhaps provide some benefit to Michael.