He could always ask, but it might not occur to Jun to do so.

"If I win, I'll get to end this. You'll get to stay here in Liminal Space or go to another world. I assume you, being freshly dead, would not want to go back to your world, but you could surprise me that way."

Death takes a good look at Jun, then adds, "Just keep doing what you're doing. You represent my virtues well enough. That's why I chose you, after all."