Kinda? I think year to year stuff dies and turns to soil. At geological timescales, a forest adds a millimeter of soil over however long it takes, eventually that dead stuff turns into coal and oil. Can't quite dredge up the memories of nurse logs for evidence though.

I mean, we're not going to do that. Forests won't save us from global warming. But I'm pretty sure that's one of the mechanisms so much carbon got tucked away.