No. The relatives are not liable because they are relatives or beneficiaries. The income tax debt is payable out of the deceased's estate. If there's no money then the debt can't be paid.
Your friend's relative may think that they are being pursued personally because money bequeathed to them may be subject to inheritance tax when they receive it; in the absence of any provision in the will that gifts are to be free of tax, that is that the estate pays any tax and the beneficiary gets the full amount, that's what happens