If unconditional friendship occured, it would have to work in terms of chance. Let's say the animal being tamed is a wolf, when you feed it until it is a companion you would have a (let's say 1/500) chance of befriending it, giving you unconditional love (this could be demonstrated with an animation above it, like small hearts). This conversion from friendship instead of companionship would only occur on the last piece of food required to tame it (i.e. when it starts viewing you as food source), so if your lucky enough once you feed them it should start giving a "-Small hearts" animation, if not it would not show any animation and just turn into a companion (seen as they follow you after moving a few blocks from them). Stronger animals would have less of a chance of giving unconditional love, with weaker ones having more of a chance. This would not only be fair, but also be realistic since animals that are weak on their own (such as dogs) usually like to be in packs, so they are more eager to find a pack to be in. More stronger animals (like lions) see themselves as not needing help, easily being able to do things on their own so their friendship is harder to get.
Another thing that would depend on the animal is what they are willing to eat, and how much of it. For example a wolf would eat x amount of raw bird (with x reducing if you give it a more nourishing food, like say cooked bird), while a bear might take y of only raw fish from you. This way you would have to hunt for specific foods for the animal you want to tame. Cooked counterparts of food could even raise the chance of befriending the animal to the point it gives unconditional love, but that's still an idea I'm conflicted with. Also this doesn't need to stop with just predators, herbivores could also be won over by feeding them specific plants and such, making this a viable way for introducing taming into the game without the use of collars that would somehow magically befriend an animal.