Any foreign objects made up of substance that are non-reactive can end up embedded in our bodies. Most obviously, there are medical devices that might permanently be left there: screws, prosthetics, artificial meshes and valves and membranes, etc. There are also some foreign objects that come from trauma, like shrapnel. Even tattoos are foreign pigments placed in a particular layer of skin that the body doesn't have a mechanism for clearing out.

But generally speaking, if our body doesn't have the enzymes to break down a substance into constituent compounds small enough to transport out, or if that foreign substance sits in a place where our body doesn't have a mechanism to actually get to, it stays in the body.

The reason why we're talking about microplastics, though, is that these compounds might actually be more reactive than previously assumed. If the plastics don't break down at all, then there's no chemical reaction byproducts to worry about. But if they break down very slowly, and the products of those reactions interfere with our biological processes in those tiny quantities, then we have a problem.