Nice question. The short answer is yes. As long as the error 404 URL has internal/external links pointing to them, Google will eventually visit the page. We can check this through:
- Google Search Console: we can see errors from several months ago.
- Analyzing server logs: we can see searchers visiting error 404 and 410 pages after those URLs were deindexed.
Maybe they could have an end date for checking an error but if that were true, once a URL is marked as gone it would never show up again in searchers (except if it gets new links). In my opinion, that way is far more complex than checking all URLs and classified the good ones and those which generates an error.
The reality is more complex than a yes/no answer. In this experiment, they tried several methods for deindexing URLs and in the last column, you can see a yes/no option whether the URL was visited after the deindexation or not.