So, living objects can regulate the amount of carbon-14 specifically, not just carbon in general? And then, knowing the ratio of carbon-14 in a living creature, we know how much time passed by? Or is it that it breaks into nitrogen that reduces the overall amount of carbon, and this is what we detect?

Because otherwise it shouldn't matter whether they died and carbon-14 broke down for a thousand years or carbon-14 broke down for a thousand years and then the recent creature consumed it. The ratio of carbon isotopes must be the same, as carbon-14 would decay anyway.

Here I assume that whatever happens with carbon-14 in fossils also happens with any carbon-14 around us. It's not that it breaks down in fossils specifically, but not in everything else. So the order shouldn't matter, unless the ratio is different in a living organism. As a matter of assumption, that is.