Everyone knows, Google from time to time will try crawling 404s - it is normal and expected. But does that impact your crawl budget? John Mueller of Google says it does not.
On Twitter, John wrote that Google will "generally crawl those URLs after we've crawled the important ones." Meaning, first they prioritize your crawl budget on your more important URLs and if there is more crawl budget left, they may go ahead and use some of that to try old 404s. John added "so nothing is used up" in terms of crawl budget in this case.
Here is the tweet:
@miguelpau @davidwkelley @googlewmc We generally crawl those URLs after we've crawled the important ones, so nothing is used up.
— John ☆.o(≧▽≦)o.☆ (@JohnMu) May 11, 2017
If you click through, you can see the back and forth on this question but generally, when Google crawls 404s, that means you have extra crawl budget - which is probably a good sign for your site. So maybe a spike in 404s mean you have some excellent crawl budget expenditure for your site?
Forum discussion at Twitter.