With the Hunger-System is based on saturation. The saturation is a value between 1 and 100, where 100 is the best and 1 is the worst. After a period of time (can be set with the
MyPet.HungerSystem.Timesetting) the saturation decreases and affects other stats of your pet.
When a pet respawns it won't have full hitpoints when the Saturation is below 90. This table shows how much the saturation affects the hitpoints on respawn:
The lower the saturation the less is the range of the beacon effect.
The lower the saturation the slower your pet will run when you ride it.