This sounds like a terrible idea for an ability... I don't understand the point in an ability that makes it look like a Pokémon is faint.
If you can explain the point or reasoning then maybe I could agree, but it just sounds silly... A Pokémon could have such an ability in the Anime because it could be a sign of trickery within a battle, but a game won't be able to understand any of that unless told.
Elaborate on what you mean by "playing dead", as it initially sounds preposterous, as the opponent would know that the pokemon isn't fainted.
However one way you could go about it would be sort of like roar or baton pass, perhaps the ability could be something like "If the pokemon should lose more than 1/3 of it's max HP the pokemon instead loses 1/4 of it's max HP and then the pokemon would pretend to faint, and you choose another pokemon to be sent out; all the while having the pokemon still alive and possibly cured of status effects."
I don't think this way would work as intended even if I thought this ability was a good idea.
If anything I'd have said if a Pokémon lost more than 3/4HP, then said Pokémon with the ability "Play Dead", should lose all HP... PROVIDED, the trainer has at least 1 Pokémon remaining... Once the faint message has been displayed, switch Pokémon out... After 2 or 3 turns (
or until the switched in Pokémon faints itself), said Pokémon with the new ability should return to the battle, displaying a message saying "
Poochyena has returned to battle because of playing dead", or whatever... With half HP returned (
or something)
But even with that in mind, I still don't think an ability like this could work... If you want an ability like this, I'm sure someone will help, but I guess the title "
discussion" makes people talk lol.