A lot of zoos use "fallen stock" from local farms for feeding carnivores: animals which have died on the farm/stables in any other way other than humanely, by a licensed slaughterman.
I remember our Head cat man at Port Lympne having an accident in his Land Rover after having been out to pick up a couple pigs.... when he came round in the crumpled mess of his vehicle there was a little old local man shaking him asking if he was ok....... and then added "sorry mate, but I'm afraid your pigs have had it!!"
Elephants, especially in colder European & North American climates should be a lot more expensive to house..... indoor heated yards etc...... but sadly in a lot of places are not.
I agree, there are elephants that are kept in some very cramped concrete cells in the winter. They should be more expensive to house in the winter.