I have found a number of 404 errors in example.com which URLs should be in en.example.com, ...
If this is a 100% fact in your situation, then you need to implement permanent redirects. You can set up automatic redirects with your server software to automatically redirect guests from example.com/englishpage/whatever to en.example.com/englishpage/whatever.
Just ensure that when you are done, you try accessing your old link in webpagetest.org or similar tool to ensure the redirect is in place. From a web browser's point of view, the redirect page will normally have HTTP code 301 which stands for "Moved Permanently".
If there are URLs that just aren't supposed to be there anymore on your server, then use the HTTP 410 status code to represent "Gone" so search engines don't keep scanning the page.
As for the remaining HTTP 404 error pages, just fix the URLs so there is content.