Download Blogspot blog in HTML

Put the posts that you want to be private into a separate blog, and make it private (Settings > Permissions).

If you want, put links to the private blog into the public one, along with comments about who is eligible to see it.

Just remember that private blogs may not be as secure as you think - see here for details: http://blogger-hints-and-tips.blogspot.com/2008/02/restricting-your-blogs-readers-isnt-as.html

You - or the person concerned - needs to remember enough details to convince Google that they really did create the blog.

There are links to the forgotten password process (that won't work without access to the email), and to the account recovery exam, here:
http://blogger-hints-and-tips.blogspot.com/2010/11/deleting-blogs-and-blog-posts.html

You / they are welcome to take the account recovery exam as many times as you / they wish: some people report success after the 3rd or 4th attempt.

Remember, the flip-side of this question involves people pretending they made blogs that they didn't really make, and asking to have them taken down just because they don't like what is said.

And if they cannot manage to take the blog down, the other option is to load other stuff on to the internet which will put the undesirable content further down the search-engine result pages.