Elderly and exempt?

Mrs X's income includes UK and widow's pensions as well as exempt foreign pensions and UK investment income. Some of this is taxed at source; some is received gross. Mrs X is now 88 and not in good health. She has not been asked to file a UK tax return for many years — if ever — but is known to HMRC as she receives a coding notice for her widow's pension each year.
It transpires that no one has checked as to whether or not her aggregate taxable income is such that she may have had a residual basic rate or even higher rate liability on her investment income. It seems the family were assuming that HMRC would not get excited about this after she dies even though inheritance tax is likely to be paid depending upon how much longer Mrs X lives. Is this is a...