What if you had a site with adsense on it but it is no longer up and running? Will you still get paid for the clicks even though Google can no longer view the ad placements and what not?
Um, how would Google SERVE ads to a site that isn't up and running? I'm assuming you are talking about a site that no longer exists, i.e. with no hosting, right?
The only way you can get paid with a site that is no longer being hosted is if Google has cached your page, in which case Yes, you do still get paid when someone clicks on the cached ad. Once the cache expires, you'll no longer have ads on a non-existent site.
But here's an interesting question: If Google found out about it, could you get banned from adsense on a cached page with your adsense ads on it which violated Adsense's TOS? Bummer for the person who gets caught with invalid clicks on their page cached with an Adsense violation before they realize or got around to changing it/removing the page, etc!