Trees never stop growing. A tree needs to grow in order to survive, that's just the way they are made. Humans and most other animals can stop growing after reaching a pre-set ideal size and just maintain themselves by repairing damage.

Trees however can only repair damage by adding a new layer of growth around the outside of the trunk. They have no mechanism to actually repair internal damage the way that humans do. That processof laying down new growth is why we can see growth rings in trees. And because they need to lay down that new layer of growth they need to also grow bigger trunks regularly. If a tree ever stops growing it will be unable to repair itself and it will die.