There isn't really a mechanism for removing broken links in WordPress, per se, unless it's something that you can really control by deleting a post or page for example.
My first suggestion is something that's worked for a lot of people: http://perishablepress.com/redirect-wordpress-feeds-to-feedburner-via-htaccess-redux/
There are also a couple of plugins out there that can help you with this, namely:
As well as a slew of related forum posts: http://wordpress.org/search/remove+broken+links
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