Relic Castle

I saw a neat little "death" feature in a Pokemon fan game, where the entered Pokemon doesn't faint if it loses but instead "dies" and cannot be revived in a Pokemon center. The status is changed to "dead" and it remains fainted in the party even after a Pokemon center heal or being deposited into a box. I would like to know how to recreate this.

I know there are easier ways to represent a "dead" Pokemon, but I'm interested in recreating this status change.

My fan game isn't a Nuzlocke, but I think having an extra layer of challenge, such as Pokemon death via permanent status change, would have its use.