In short, when you're training for an endurance sport, as triguy said, the fast twitch muscle fibers will convert to slow twitch, but this also depends on distance. Take this for example:
You run 7 miles a day at 7 min pace and you've been doing this for about 2 years now, your body is adapted. To increase aerobic capacity, you either need to increase your mileage of daily runs or increase the speed at which you're running your daily runs. Either scenario will exhaust fast twitch fibers that were never exhausted before, turning them into slow twitch fibers basically.
If you think you're burning muscle, this only happens in extreme cases where your glycogen stores are completely depleted and you have very little fat for energy. Any decrease in weight or muscle you see is a result of the fast twitch converting to slow twitch basically. This is an oversimplification, but I hope it helps.