Change url / unpublish?

I want to temporarily ‘pseudo-remove’ site contents – have it unavailable to search engines and direct traffic, but still visible to myself through a new url.

My plan was to change the site address to something like ‘/old’ – figuring that inbound links from seach engines and elsewhere would then be delivered a 404, on which I could explain that stuff was temporarily unavailable.

But this doesn’t work – inbound links from Google still work at the former address.

What’s the fix?