Eating only protein can sometimes be dangerous for some people and can increase the risk of developing heart disease.
The risk of heart disease comes from the saturated fat that some high protein foods contain so you should keep a check on your health when eating just protein.
Many people do survive and stay healthy on a protein only diet but you should really speak with your doctor first before going on a protein only diet.
Your current health can affect whether the protein only diet may harm your health as well and if you have any existing heart problems or high blood pressure etc then I would not recommend eating the all protein diet.
Eating only protein can also increase your weight gain so you may get fatter especially if you do not exercise much after eating the protein only diet.