Cauldron Haze

If a creature with persist that has +1/+1 counters on it receives enough -1/-1 counters to cause it to be destroyed by lethal damage or put into its owner’s graveyard for having 0 or less toughness, persist won’t trigger and the card won’t return to the battlefield. That’s because persist checks the creature’s existence just before it leaves the battlefield, and it still has all those counters on it at that point.

If multiple creatures with persist are put into the graveyard at the same time (due to combat damage or a spell that destroys all creatures, for example), the active player (the player whose turn it is) puts all of their persist triggers on the stack in any order, then each other player in turn order does the same. The last trigger put on the stack is the first one that resolves. That means that in a two-player game, the nonactive player’s persist creatures will return to the battlefield first, then the active player’s persist creatures do the same. The creatures return to the battlefield one at a time.

When a permanent with persist returns to the battlefield, it’s a new object with no memory of or connection to its previous existence.

If a nontoken creature that gains persist this way is put into a graveyard, that card will be returned to the battlefield with a -1/-1 counter on it. However, because it’s a new object with no relation to its previous existence, that permanent will not have persist.

If a creature has multiple instances of persist, the result is largely the same as having just one instance of persist. When the creature is put into a graveyard, each persist ability will trigger. The first one to resolve will return the creature to the battlefield with a -1/-1 counter on it. The rest will do nothing.