It is not possible for a tree to survive if the entire inner part, including the heartwood and sapwood, is missing. The inner part of a tree is vital to its survival and health, as it is responsible for transporting water, nutrients, and sugars between the roots and the leaves.
However, it is possible for a tree to survive if only part of the inner part is missing. Trees have a remarkable ability to compartmentalize damage and decay, which means that they can wall off or isolate injured or infected parts of the tree to prevent the spread of damage to the rest of the tree.
For example, if a branch is broken off or a section of the trunk is damaged, the tree will form a boundary around the damaged area and begin to grow new wood to replace the damaged wood. This process is called compartmentalization and helps the tree to limit the damage and prevent the spread of decay.
It's worth noting that the extent to which a tree can survive damage to its inner part depends on the severity and location of the damage, as well as the overall health of the tree. Severe damage to the inner part of the tree, such as from girdling or extensive decay, can weaken the tree and make it more susceptible to further damage or disease. In some cases, such damage may even be fatal to the tree.