Crucial warning: Adobe no longer hosts Reader XI on its official website. Any site claiming to be "official Adobe" for this version is fake or dangerous.
However, if you have a legal reason (e.g., running on an isolated test lab or legacy contract), here are the least-risky sources:
The Internet Archive (archive.org) crawled Adobe’s download pages. Search for "Adobe Reader 11.0.23" and filter by software. You may find a cached installer, but verify the file hash (see Section 5 below).
Before you rush to download Adobe Reader XI 11.0.23 offline installer, you must understand that Adobe ended support on October 15, 2017. Here’s what that means: