Like Bart said in a comment, this shouldn't be too much of a problem. If a link dies, the content should already be included in the answer, so that the link should not be necessary anymore.
If you find that there is a widespread problem of "link-only" answers on your SE sites, you should either edit those answers to include the important information, or flag it as "not an answer."
That said; as Servy pointed out, this would be a massive undertaking, which would involve a lot of resources that SE just might not have. There are a lot of links around, and caching them all is a lot of information that, as mentioned above, shouldn't really be needed.
I don't think that this feature is a good, or necessary, idea.