This is Cursed Tier 2, after I've already killed Veytharion. I was just grinding to do the Bus relic at Round 60.
There was nothing to interact with in the arena. The ammo box still worked. I was able to do teleport back out by using the pad to teleport to Tessie.
I did finish the round in the arena and a new round started (it was incredibly easy in the arena).
My only regret was not trying to jump in a kazamir again.
After I got back into the map, the mystery box was not anywhere on the map.
If you have anything you'd like me to try, let me know. I have the game in my save file.