Where do researchers get the money to replicate others' work?

I'd like to follow up on my previous question. If scientists have to replicate and validate/refute their peers' research, where do the "provers" find funding?

In my 2 years as an undergrad at a public American university, I've heard of a lot of professors researching new things and/or trying to find funding to research new things, but I've never heard of a professor dedicating resources to replicate his/her peer's work.

As I explore existing literature for my research project, I see that I could have used existing literature to guide the experiments I did for my project. Along the way, I could have replicated + validated* the existing "new" methods before trying my new method. Is this how researchers usually review their peers?

That is, professor X gets a grant to explore field A. Professor Y comes up with model 1 for field A. Using his own funding, Professor X designs and conducts an experiment to replicate model 1 before testing his own model, model 2.

Note: I assume my question depends on the field of study since a computer scientist can more easily verify a model + experiment than a chemist.

*Is there a better verb or phrase for replicate + validate/refute? Or does validation imply replication?