What happens to the nitrogen in a rabbits body
when it dies

When rabbit dies, the nitrogen in the rabbits body is released into the soil  by decomposition.

Explanation:  

When rabbit dies its body is decomposition takes place. Decomposition is process of breaking down of the dead remains of the plants, animals and insects into tiny pieces by free living bacteria, fungi and worms present in the environment .

During the decomposition process the nitrogen present in the dead rabbit body is released into the soil in the form of ammonia. The bacteria(nitrifying bacteria) present in the soil converts this ammonia into nitrates so that it can be again used by the plants. Now plants intakes this nitrates for photosynthesis process. This process of fixing nitrogen back into the atmosphere is called nitrogen cycle.