Q:

What happens when you lose in an Arena

When you lose in combat, generally your body is left behind for you to collect.
In the the Arenas added by the 3C3C1D119440927 DLC found in the Desert, Flooded City, and I assume Forest (haven't been able to access it myself) the place where I fight can't be accessed unless I choose to enter the fight.
So what happens if I lose in these Arenas? Do I leave a body behind like I normally do? If so, how do I then regain my body?

A:

I just tested this to be sure.
When you lose in the Arena, you're not actually dying, so you don't leave a body behind. You're merely losing the trial. After failing the trial, you can check this by looking at your equipped chipset. You will still have all of the chips equipped as when you lost the Arena trial.

