Hi Melony. I think the process you are looking for is called neuroplasticity. Although this term can be used somewhat broadly, it is often used in the context of recovery from brain damage. When brain damage occurs, the brain (sometimes) has a pretty amazing ability to compensate by essentially "rewiring" itself. For example, new connections in the brain may occur when someone goes blind to compensate for the fact that the visual cortex is not being used to process inputs from the eyes.
It is generally accepted that this process more easily occurs in younger people, but there is also evidence of it happening in adults. I encourage you to read more about neuroplasticity. It's really cool!