Basically nothing. Most sites are hosted in shared hosting where thousands of site shared one IP. All search engine know this. However, if they are in the same industry and try to do mass cross linking then, it's considered "blackhat" (depending on how you screw it up). And, with blackhat, you may be punished and you may not. Depends on the techniques and luck.
Indeed, nothing will happen, as long as they have only the same IP, and not same owner, same content, same links. Most websites are on shared hosting, and as You can see - most of them are alive