If the client has an old link serve an old version. But have links to what will be future versions and make the client walk them. It is doable but different. Lots of stuff is static anyway, like CSS, so you can use for this and have a different process for stuff that varies.
But as the grandparent said, serving the old version may result in a security vulnerability. There are cases where you MUST serve the latest version, and the latest version only.