[Aachen]

I've got a domain where the previous owners just let it expire while it still had useful information on it. My solution was to 301 redirect requests to the Internet Archive so that any links continue to work for a while, while also making it obvious that the site is gone. I won't be paying for this indefinitely though, the information isn't that vital and people should learn of the archive. Hopefully this helped them do that.

The difference between the situations is that I wasn't interested in using the domain myself. Hosting the old site in a subdomain like u/Hard_Space described sounds like a good solution (I'd go for a subdomain rather than a directory, people often don't read further than the slash and it makes it feel like one site, while a subdomain is at the front and feels more like a separate part, especially when given a descriptive name).