I tried to get round this problem, after my Mum died. I took her 5! (all in moderate chaos as people were indexed as surname, first name, "Husband of..." nicknames etc, even though her mind was completely working, she often jotted people on the first page she came to .... good job she never worked as a filing clerk!!) and compiled a more-or-less accurate list, - the 'phone numbers were useless, some so old they had letters for exchanges - and set about writing to them all -it was coming up to Christmas - with a small card, and in most cases some message similar to:
"I have been going through the address books of my mother XYZ, born ABC in .... and found your details there. I'm afraid that I do not know if you have been a friend, or a relative, but I write to inform you that she sadly died on D M Y earlier this year, and as it appears that you have been in correspondence with her, I thought you might feel better to know. If you would like to contact me, my full name, address, 'phone number and an e-mail address are on this card."
And I put all the "please forward" stuff on the envelope, too....
I thought that was quite carefully phrased. No replies, although in my later researches I found out that one name (Pratt, in Nottinghamshire) was apparently the married surname of a cousin of hers. Wonder if it was......
And I still got 4 cards that I was unable to trace, for her!!