The client has updated its site and has now received 404 errors with old links / slugs

If you have completed this task without you, have the customer take care of the resolution unless he pays you to solve the problem. When they pay you, they search the error logs for all content and, if possible, create 301 redirects for the new content. There may be a plugin to do this. However, it is correct to create a 301 redirect when you move content from one domain to another or change paths in content to another path.

You may be able to create script rewriting rules to do this for you until you have optimized and updated everything, or you can change the paths to fit the previous structure. In summary, you should provide 404 error pages if there are links to content that no longer exists. If the pages exist but are in a new location, you should redirect the old path to the old content to the updated path to the new content.