One website affecting the other one (on the same host)?

OK, the title is a bit confusing, let me explain.

I have two websites on the same host. One website is doing good, and I wouldn't want to jeopardize it in any way. The second is basically dead in the water but it's getting some traffic and has some authority so I'm thinking of using it to sell guest posts (maybe even rent out some links).

Now, my question is, if the second website was to get penalized in any way, could it affect the other website that's doing good? Have you had that situation happen?

It can potentially be a problem If they're using the same IP and the same whois.