Hello!
Although 404's will eventually stop being crawled by Google, having too many at once can negatively affect your rankings. The most important thing is that you do not want to be linking to these 404s anywhere from within your site. If so, you want to definitely remove those links.
If I have one or two 404s in my crawl errors, I typically will just leave them be and wait for them to be dropped out of being indexed. Some other solutions I've utilized are:
1. Make an engaging 404 page so that when users find the page they will be encouraged to stay on the website. Having a search box or some of the most popular links on the page is a good place to start
2. 301 redirect the pages to relevant pages that do exist. This will help your link juice flow and will make for a good user experience since they are reaching a relevant page.
Hope that helps!
