Google’s John Mueller said on Twitter the other day that crawl budget is technically used when Google tries to access 404/410 page not found URLs. We did report a few months ago that crawl budget was not used in these cases but specifically because those crawls tend to be done only after the normal crawl is done and there is left over crawl budget to be used.
But if Google does try to access the 404 or 410 page, it is technically using crawl budget to do so.
Here is John’s tweet:

They use the normal crawl budget, but we tend not to refresh them so often since they don’t “change” that much.
— John ☆.o(≧▽≦)o.☆ (@JohnMu) September 9, 2017
But again, this typically only happens when everything else Google wanted to crawl on your site was crawled already.
Forum discussion at Twitter.

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