I could swear I remember hearing about a variant with rules kindof like that. Vaguely, I remember that the variant involved a rule where as a turn, you could put a piece back on the board. I’m pretty sure it had to be placed on “your half” of the board. Like, you couldn’t just place it right on the square right next to the enemy’s king when the enemy’s king hasn’t even moved yet.

I don’t recall for certain whether it was your previously captured pieces that could be respawned (like, if your rook was captured, you could respawn it) or something more like you could spawn a piece of your enemy’s that you’d previously captured (like, if you’re playing white and you capture a black knight, you could spawn an additional white knight on your side of the board).

And I can’t remember if that variant had any particular name.