Only if you don't violate the copyright of the dead person - which, depending on the country, can last 50 to 90+ years after the person's death. Thus to publish you'd have to get the right to do so from said person's estate.
There are many instances where private correspondence, etc. has been banned from publication/the public domain for this reason.
How about this for the plot: Witness a high profile crime & then get a witness protection just to avoid getting tracked by FAANG! :)
https://www.itv.com/news/2021-01-18/woman-ruled-dead-in-2017...
There are some resitcitions there, for example the Private letters and Diaries would still be covered under copyright and the estate of the person could come after you for Copyright violations if it was with in 70 years of their death.
Also the Estate of a person could absolutely sue you are defamation provided the Estate has a person actively working to police that activity and the resources to hire a lawyer to do it.
So your position that "dead people have no privacy" is really false as they have just as much privacy as people alive it is just most dead people do not have anyone around that will expend the resources to enforce it like a live person
The relatives of the deceased can sue you for defamation damages to their reputation (e.g. the widow might assert that the claim about her deceased husband damages her own personal reputation, and if so, perhaps she would have standing but only as far as her own name was slandered). The relatives or the estate can not successfully sue you for defamation of the deceased him/herself.
This is a decent precedent - https://law.justia.com/cases/massachusetts/supreme-court/vol...
The situation in UK seems to be the same - https://www.holdthefrontpage.co.uk/2012/news/mps-rule-that-y...
This article lists many interesting famous situations from history - https://jonathanturley.org/2007/08/18/defaming-the-dead/
It's even possible that defamation that happened while the victim was alive gets ignored if they die before the case is settled - for example, Ohio code (http://oh.elaws.us/orc/2311.21) explicitly asserts that libel and slander cases (unlike pretty much everything else) should end in this case.
A famous case is Michael Jackson and the 2019 documentary "Leaving Neverland"; when he was alive, he successfully won a defamation case against Victor Gutierrez with a pretty much equivalent case, however, as this happened after his death, those managing his estate were not able to bring a defamation suit for this documentary because those defamation laws did not apply any more.
Law stackexhange has a quick summary at https://law.stackexchange.com/questions/28842/can-you-libel-...