Inheritance is not taxed, and the sale is on your PAN, not theirs
Two facts remove most of the worry. First, India has had no inheritance or estate tax since 1985, so simply inheriting the property or the accounts is not a taxable event and does not require you to file anything in the deceased's name for the inheritance itself. Second, once the property is transmitted to you, you are the owner, and when you sell it you sell on your own PAN.
That means the buyer deducts TDS under Section 195 against your PAN, and you claim that credit on your own return, where you also compute the gain using the cost and holding period carried over from your parent (Section 49(1) and Section 2(42A)). None of that needs the deceased to have had a PAN. So the sale, the TDS and the gain all run cleanly off your own PAN.
When the deceased's PAN actually matters
There is one situation where the deceased's PAN is relevant: filing the deceased's own final return, for income they earned in the year up to the date of death, or to claim TDS that was deducted in their name before death. As the heir you are their legal representative, liable to settle that final position but only up to the value of the estate (Section 159).
If your parent had little or no taxable income of their own before death and no TDS sat in their name, there is usually no final return to file and the missing PAN simply does not arise. It becomes an issue only where there was pre-death income or TDS to account for. So the first question a practising CA asks is a narrow one: was there any income or TDS in the deceased's own name that needs a final return, or is everything now flowing through you as the heir?
Obtaining a PAN through the estate, where it is truly needed
Where a final return genuinely has to be filed and the deceased never had a PAN, a PAN can be obtained for them through the legal representative, who applies as the representative of the person who cannot apply for themselves. With that in place, the legal-heir registration on the income-tax portal, which is built around a deceased who had a PAN, can be completed and the final return filed.
This is a specific, document-heavy step, and the exact portal path for a parent who never held a PAN is not a common one, so it is worth having a CA handle it rather than attempting it blind from abroad. In practice, though, most NRI heirs find they never reach this step at all, because the estate is settled and the property sold on the heir's own PAN, which is the ordinary route.