I believe the answer is that;Corals are stressed and more likely to die without zooxanthellae; the zooxanthellae grow best when associated with the corals.
The corals and the algae have a mutualistic relationship. The coral provides the algae with a protected environment and compounds they need for photosynthesis. In return, the algae produce oxygen and help the coral to remove wastes. Most importantly, zooxanthellae supply coral with glucose, glycerol, and amino acids, which are the products of photosynthesis.