The belief that muscle will turn into fat when you stop training is something that is often bandied about the fitness industry by untrained, uneducated individuals. This is one of the biggest myths of all time.
The reason why it is a myth is that there are two different constructs at play that are made of totally different components. It is akin to saying that you can turn water into wood. It is not going to happen.
What does happen when you stop training and maintain the same eating pattern that you had while training, is that you will:
1. Start to lose the lean muscle tissue gained from the training
2. Start to increase your body fat levels as you are in calorie excess
3. Start to lose your fitness and cardiovascular conditioning
So while it appears that your muscle is turning into fat it is not. It is your body changing due to the change in your activity patterns.
So next time that you hear this myth, ask the person making the claim if they are able to turn water into wood!