Add post to category at expiration

[Shyzer]

Would it be possible to add a post to a specific category once the expiration date arrives? I have my site setup to style our Dead category with a crossed out title and an image overlayed on the post saying the deal has expired. Only downside is that I have to manually edit the post to add the Dead category to it once the deal has expired. Being able to automate this would be a huge lifesaver!