Although with the release of Google’s latest algorithms code named Penguin and Panda that arguably cleaned up search engine results pages to a certain extent, the easiest way to get your rankings up is by having lots of incoming links. The more of those links coming from reputable websites the better as ‘not all links are created equal’.
Ironically, the easiest way to get in trouble by the big G is by having ‘too many’ links pointing to your website especially if that increase did not look ‘natural’. Unnatural linking is any linking that looks like it’s been done by a machine, computer, an automated script or alike and not humans.
So the questions was posted to this search engine giant as to what happens to your website if you end up buying links from a website that subsequently gets caught selling links which by the way is against Google webmaster guidelines. The answer to that question was really what was logically expected to happen (define logical though!)
Basically, if your website was benefiting in rankings from the link/s from that website, you will just loose that SEO juice stream. What I mean by ‘just’ is that the big G is not going to penalise you per se but just remove any value your website was getting from it.
Here is a short minute and a half video on it explaining it further.
As to the question ‘should I buy links’ see my article here.