Yes, a tiger is going to eat grass.
Hmm, let's think on this.....If a tiger no longer needed to hunt and chase prey, it would no longer need it's razor sharp claws, muscular and agile body, or amazing senses. Over the generations, such qualities would no longer be useful or necessary, and would therefore not be worth the energetic expenditure to grow and develop. Every physical attribute an animal posses costs the animal in energy to maintain.
Assuming that principle remains true in paradise, what qualities would be useful in that scenario? Well, the teeth would need to become flatter to adjust to the vegan diet. The body would no longer need the immense muscle and physical agility, but rather a good slow grazing body plan that maximizes the available digestive capabilities. All those honed senses? Too expensive. A much simpler set of basic senses (enough to see the grass in front of your face) would suffice.
Essentially, if the natural world still functioned in a somewhat similar manner, paradise would turn all majestic tigers into big stupid cow-like creatures in relatively few generations. Evolution's a bitch.