You still get the money.

A long time back, my site went out of service for days, and I was still making money for the Google cache. (but now I don't allow my site to be cached)

I looked at the cache pages at archive.org from one of my sites going back about a year, and it did not display the AdSense ads at all. I looked at the source code and the AdSense script was there, but they must have it blocked from displaying.

I was looking at one of mine and it did show the ads. Just kind of creeps me out that clicks generated from my work benefit others, whether they get the money or not. The advertisers get the visitors and Google probably gets paid no matter where the click is generated.

who is "others"?

If ads show, then you will get the money for any resulting clicks.

As previously mentioned, archive.org doesn't seem to show ads at all. If you look at the source code you can see why: Google has blocked them from archiving the relevant JS file.