Almost 20 years ago, I worked with this (not particularly competent) sysadmin. Policy said the root password had to be rotated once a month. So, in July 2003, they set the root password to blah0307 (where blah was some random word, which I forget now but knew at the time.) I wasn’t actually supposed to know the root password, but one of my colleagues let me in on the secret, including the repetitive pattern. I think the security auditor ticked the box “root password changed every 30 days”, but never asked what the password actually was.

I know some places have rules like “must have at least N characters different from previous passwords”. However, depending on the exact rule, people can come up with easy-to-remember workarounds: e.g. the “blah” bit is ”foo” in even months and “bar” in odd ones.