Well, I'm not sure which ruleset or specific shape shifting ability he's using. They work in various ways. Some come with their own, separate HP pool, some retains what you had, and some heals you, so severe injuries may or may not carry over. Some of those are spells of relatively high level (too high for these characters), or abilities limited to similar forms. Too many for me to keep track of, at any rate.
Transformation spells and abilities tend to work in the same way in D&D. Things transform with you, and if you get knocked unconscious you revert to your true form. It differs a bit whether your HP while transformed is a separate pool or not, and what stats carry over (physical stats transform while mental stats sometimes do, sometimes you have your original stats).
