What would most likely happen to a person who is not getting enough essential amino acids in his or her diet?

The correct answer is - muscle tissue would break down to supply amino acids. You can easily answer this question if you apply the system of elimination. Our bodies cannot synthesize essential amino acids, there would be dire effects if this happened, and we don't have protein stores in our body. This leaves us with one option only - since amino acids are necessary, the body has to get them somehow, even if it meant breaking down muscle tissue.