Is the cherem applicable after the death of the letter writer? Are the yorshim allowed to read private letters written by the deceased?
My apologies that it took some time to get back to you.
There are a number of reasons given for the Cherem D’rabeinu Gershom not to open other people’s private letters etc. The Halachos K’tanos (1-276) says that it is because it is rechilus to reveal other people’s secrets. The Toras Chaim (3-46) says that it is because of geneiva (or geneivas daas), and because of mazik, as very often because it causes damage to the other person. In shut Chikikei Lev Y:D 49 D:H U’mata) says that it is because of vahavta l’reiacha k’mocha, to be considerate of others.
Regarding the yorshim reading the letters or documents of a deceased person, it would not be geneiva, because his property went over to them. Nor would it be because of v’ahavta lrieacha, because it doesn’t apply to a deceased person. However the reasons of mazik could apply to a deceased person, whose name can be damaged, the reason of rechilus would also apply.
A number of poskim have ruled that the yorshim may open letters etc. that they think might be beneficial to the niftar, either a tzavah, or something else that he would want them to know, but if they see that it is something he would not want them to read they have to stop. Additionally, some poskim were of the opinion that if the niftar was an older person, who knew that eventually his children would see his letters etc. it cean be assumed that if there was anything there that he truly wouldn’t want them to see, he would have already destroyed them. This however would depend on the individual circumstances.
Ma’adanei Yom Tov 2-46, Teshuvos V’hanhagos 3 387, R’ Y. Scotzlos shlit”a in the name of a number of poskim, R’ B. Forst shlit”a. See Maadanei Yom Tov who has a different opinion on this.