Is it bad to change slugs for SEO and will the Google crawled page
example.com/apple be broken?
Yes to both.
When you change the slug /apple to /banana, as you indicated, the URL changed from:
When URLs change, Google will need to find and crawl them again (URLs are the addresses of your pages used by both search engine bots and search engine users alike).
It will also evaluate the new URL
example.com/banana based on how well the keywords appearing in your page match the rest of the content - so if "banana" is not a good match for a previous page discussing "apples", that keyword would not fair as well.
One way you can mitigate this is to make sure you 301 redirect previous slugs to new slugs, and edit your Sitemap and resubmit it. You should also be sure to check your other pages for references to the previous URL slugs to update them to the new ones, and try to contact other sites to update them as well.
You could also use the Fetch as Google tool to speed up the crawling of the new URLs.