How to implement link checking in the content a CMS stores

For those of you that build CMSes, how do you handle the checking of links
within the content of the CMS.

For instance, you have page content stored in a DB record. This content is
formatted HTML, and has a link to another page on your site. This other page
is later deleted, and now you have a bad link.

I'm guessing the weak link here is storing URIs as hard-coded in the HTML.
Are there practical alternatives to that? If not, are there any products out
there that folks would recommend that would scan the site externally looking
for bad links? 

-Darrel