[creat0]

If you wanted your personally identifiable data protected from public access (being cached by search engines), then presumably you would not submit it to a web site that is open to the public (not password protected).

If Craigslist changes its name or sells its SF apartment listings to some site with a name you do not like, what can you do? Answer: Nothing, because you gave them an exclusive nonrevocable license to your data. If you really wanted control over your personally identifiable data then it would probably be wise not to submit it to a site that gets scraped and cached by Google (from which anyone can make fair use) and certainly not under a license that gave you no control over the data after it's submitted. You would want a site that has some sort of protections like passwords, that allows some degree of pseudo anonymity so your name is not embedded in an evergreen search engine cache; and you would want the right to tell the site to remove/delete the data at your direction, if that became necessary (e.g. in your example scenario).

In short, Craigslist really isn't in the business of protecting your data for you. Its terms are what they are because it's seeking to protect its own business, which relies on your data.