If my active Pokémon is asleep and my opponent's defending Pokémon gets knocked out from poison, what is the order of flipping for sleep, taking my prize card, and my opponent promoting a new Pokémon?
The action of KO'ing a Pokemon between turns is the very last thing to do between turns.
So, the Poison damage is applied and the Asleep check is done in either order, it doesn't matter.
Then the KO is checked for, and the Pokemon put in the discard pile.
You draw a Prize card and your opponent then promotes a new active.