Automattic has been working with the Internet Archive to develop a plugin to combat link rot, and it’s a plugin I’d encourage you to install. As the plugin says:

When a linked page disappears, the plugin helps preserve your user experience by redirecting visitors to a reliable archived version. It also works proactively by archiving your own posts every time they’re updated, creating a consistent backup of your content’s history.

I’ve been doing this manually on my old archives, fixing broken links and tending the garden. But we can make it all automatic.