Comment by ldoughty
I agree it probably isn't a great idea to publish it... I'm guessing some malicious actor could find a way to use this information to fiddle with the remaining benefits their family might be receiving...
That said, the _typical_ things an SSN is used for would not be terribly useful for someone that's been dead >2-4 years... Automated checks should flag e.g. credit applications as being for a dead person :-)
Social Security Admin publishes a master death file containing a list of SSNs of those who have died. This is how institutions know to close credit, deposit, and brokerage accounts; they subscribe to and consume the file. Some copies of it have been uploaded to the Internet Archive when someone has obtained a copy (cost to obtain from NTIS is prohibitive for individuals, but reasonable for commercial customers).
Broadly speaking, right to privacy evaporates at death, and when the Machine is working properly, SSNs have no value once they have been marked as deceased in SSA's system of record (as that flows through to various gov and commercial systems to ensure benefits cease and next of kin processes kick off for anything of value).
https://en.wikipedia.org/wiki/Death_Master_File
https://www.ntis.gov/ladmf/ladmf.xhtml