Comment by lithocarpus

They do, and, mostly they will eventually rot and release the carbon back - but it may take hundreds or thousands of years - if ever - for a forest to reach equilibrium where it's emitting as much as it's accumulating.

One way humans can improve on this is by making charcoal out of wood and burying it or just spreading it on soil. This drastically improves the fertility of the soil improving the rate that that soil can sequester carbon by growing trees even faster, and, as long as the charcoal is mixed in soil and not in a huge dry pile on top where it might burn, this process need never reach an equilibrium and can keep accumulating more and more carbon, more and more fertility and water retention capacity, more and more abundance of food production. This is what the ancients did in making terra preta in South America and similar charcoal-infused soils that have been found all over the world.

We do this where I live in California. It's a way to reduce forest fuel load while increasing carbon sequestration and fertility. Only cost is labor. It's theoretically possible to do at large scale with machinery instead of people, though the attempts I've seen have not proved viable. For a low expense human-scale way to do it, just making big piles and burning them from the top down (so no smoke) - piling more and more fuel on as it burns, and then dousing with water once it's mostly a big pile of coals, works quite well. With the addition of a big metal ring for a kiln, efficiency can go up even more from (very roughly) 50% of carbon turned to charcoal, to maybe 80 or 90%. Numbers vary considerably. But in all cases, the amount of carbon moved from the rotting or burning cycle to permanently sequestered is significant.

Compared to the short term carbon sequestration of building things out of wood (99% of which will burn within a few centuries), these soils have lasted thousands of years. There must be some mechanism that will eventually recycle this carbon back to the atmosphere but it may be on the timescale of hundreds of thousands of years for most of it.