The Relational Clause and the Case

In Russian, the case comes from the role in the relative clause. For some reason, I was thinking of a situation where you could have it agree with the case in the matrix clause. Is there a language that ever does that? It doesn't make a whole lot of sense to do that way. The closest phenomenon I can think of is, uh, raising,. You'd say something like I, I want him to eat where him is the subject of eat. But, um, it's getting its accusative case from the matrix verb and so it looks like an object.