The brain is capable of healing itself after some trauma and brain injury by regrowing and rebuilding the dead brain cells but that can take a long time.
Also it depends on how severe the brain trauma is as if it was very severe brain trauma then the brain is unlikely to ever heal itself and repair itself completely enough to allow the person to have full brain health.
After severe brain trauma the person could be just like a vegetable and may not be able to speak, write, walk etc or do any of the normal tasks they would have been able to do before the brain trauma.
So if the brain trauma is not too severe then the patient may recover and be their normal selves but with more severe brain trauma the chance is less.