Inbound links drive traffic and rankings. Inbound links are precious. Allowing inbound links to fail on nonexistent pages is a marketing crime.
Once you've found your inbound broken links, you can contact the site linking to you to fix them. Smarter: handle it on your side, routing the traffic where you want to send it by (re)creating the appropriate page. Smarter still: issue a 301 permanently moved redirect and flip the traffic to where it should go.
Ignore broken inbound links long enough and they'll go away. Bad. Sad.
Thanks, Google engineers, for these valuable data.
Link: Helping Website Owners Fix Broken Links, GoogleBlog