On the default official server settings: Whilst animals are in the animal pen slots they do NOT have any hunger timer … they can stay in there forever without food …
Funcom removed the hidden death timer on the animal pen adult pets.
Once removed from the pen into your inventory then they have an expiration timer on them. If you put them in an preservation or improved preservation box which has one piece of ice in it, then the timer is halted just like the boxes do for any item with a decay timer.
Once you have placed them from your inventory into the world then the feeding mechanism starts and if not fed their hunger bar will slowly start to decrease and when it reaches 0, they will start to take damage and then die. They should take up to 5 pieces of any raw food item from a feed box on a regular interval to maintain hunger bar at 100/100. If they are not then re-arrange the food in the feed box.
For your situation, I suggest that you place food directly into the inventory of the greater crocodile that you have placed into the world … I have a greater crocodile that was tamed in a tier 3 pen out in the world consuming food as normal.