It's actually pretty simple.
Trees are not weeds. Only the outer layer of a tree is alive. The innards are dead cells that only serve as an skeleton.
That's why you kill a tree by peeling a ring around the bark.
Then again, while a hollowed out tree can keep on living without issues, it's very likely that the beings that will take root there could potentially overwhelm by rotting it from the inside out. Bacteria and fungi can easily get it sick.