Buried. There is absolutely no evidence that most animals in properly sized habitats at zoos have any desire to leave. Animals escaping are very rare, and I know of at least one instance where a monkey cage was left open, and the monkeys went over and angrily tried to slam the door shut over and over until somebody locked it again.
Why would they want to escape? Almost all animals are driven toward the opposite of our conception of "freedom." They have short ranges, they mark their territory aggressively and stick to it, and they are most highly motivated by food and safety. A zoo enclosure provides free food, extreme safety, and a perfectly delineated territory that will hardly ever be invaded. With the exception of migratory birds, and a couple other species (including humans, who were nomadic), this is heaven for animals.
The cages are there far more to keep humans out than to keep animals in. Thinking otherwise is simply the result of people improperly projecting human attributes onto animals that are in reality wired very very differently than us.
Kirk: Spock.
Spock: Ship... out of danger?
Kirk: Yes.
Spock: Don't grieve, Admiral. It is logical. The needs of the many outweigh...
Kirk: ...the needs of the few.
Spock: ...Or the one. I never took the Kobayashi Maru test until now. What do you think of my solution?
Kirk: Spock...
Spock: I have been and always shall be your friend.
[Holds up his hand in the Vulcan salute]
Spock: Live long and prosper.