It does not exist in nature, they are mutants manipulated by some enterprising/adventurous growers.
No, do not bury the dried out part below surface. Cacti may just try to heal and callus, and harden it/cork it. As long as it is staying firm, and not mushy, it may just heal naturally.
This is not the best example, but epis grow like hylocereus, so I just let the plant heal itself. I also get those brown marks below, but it will dry out and plant survives. Really important to provide good air circulation, light and warmth.
This is an epi, not hylocereus..just to give you an idea:
