Apparent death, thanatosis, or tonic immobility (TI) often referred to as playing dead, playing possum or feigning death colloquially, is a deceptive adaptive behavior where an animal appears like it is dead, i.e., freezes or becomes motionless.
Animals use it either as a defense mechanism from their predators or for aggressive mimicry, especially by parasites and predators, so that their prey and hosts do not identify them easily.
This behavior has been noted in sharks, teleost fishes, some reptiles, and even human beings. What about rabbits?
Can rabbits play dead?
Yes. Rabbits play dead, and it has been "found to be indicative of a fear-motivated stress state."  In this case, it is a bunny's final attempt to escape or avoid being eaten by their various predators.
When it occurs, your bunny is likely to lie on its back while its legs (both the hind and front) are stretched out. Their eye pupil may also dilate.
Once they recover from the tonic immobility states, bunnies tend to show signs of stress, including faster breathing and heart rates.
Besides trying to avoid being eaten, there are instances of rabbits playing dead when you hold them. The reasons are the same, they are extremely afraid. Some vets consider it a good thing since it can help conduct some veterinary procedures without the need for anesthesia, which has more risks.
However, some people note that bunnies do not play dead, they are usually scared to death. They "freeze when shocked or scared and not move a muscle for several hours if necessary." 
In such a case, you need to care for them by such as taking them under a shade and keeping an eye on him or her. These animals are known to die out of extreme fear and shock.
Finally, it is worthwhile noting that TI only happens when a bunny has been caught. Otherwise, it will run away.
Don't confuse it with rabbit flop
However, tonic immobility should not be confused with bunny flops where your bunny will roll or fall to one side as if it just fainted. Bunny flops are a natural body language, especially when your bunny is relaxed, happy, and trusts you.