Will the body go catabolic and start eating muscle tissue when you do cardio without eating?
Yes, your body will use some muscle tissue for energy but it will also burn much more fat in that process.
If your intention is to burn fat and see your abs, then, it is very hard to do that without burning any muscle tissue at all.
You minimize that through your diet by making sure your protein intake is high and your blood sugar levels are stabilized to keep you anabolic throughout the day.
Having some BCAA’s before you go out on the run will help halt the breakdown of muscle.
Cardio on an empty stomach has always helped me lean out. You should try it and see what works for you.