I don't know if you can fix dead links automatically (probably not) but there are tools like this one, which will help you find them: http://wordpress.org/plugins/broken-link-checker/
also, you must delete your indexed broken (or non-working) link via google webmaster tools > remove URLs
Use the url redirection plugin to fix your broken urls by redirecting them to a new working url. This one is best: http://wordpress.org/plugins/redirection/
Broken Link Checker is the best for this BUT run it when the site isn't busy as the plugin is resource intensive.