In 1.16, you use an item to give your tamed pet/horse extra lives.  By default the item is Rabbit Stew but this can be changed

Have you ever wanted your pets to mean something?  To stay with you, go caving, not suicide every five seconds.

This mod makes your pets and horses basically invincible, as long as you are online in the same dimension.

For game balance this means that breeding is disabled.  You will only be able to tame a pet or horse by finding one naturally spawned in the world.

Config file: 

tamedrespawn.cfg

# Configuration file


tamedrespawn {

    # If true no breeding will happen [default: true]
    B:blockBreedingHorses=true

    # If true no breeding will happen [default: true]
    B:blockBreedingPets=true

    # Send chat popup on revival [default: true]
    B:chatMessages=true

    # Apply regen on revival [default: true]
    B:regen=true

    # Apply weakness on revival [default: true]
    B:weakness=true
}